Double Helix

4-gate-sequence: Install blue gate in "j", purple gate in "f". Install orange head in "M", blue head in "E", red head in "F"
This will open a door on the red putter with a gate and a head.
5-gate-sequence: Install green gate in "j", purple gate in "f", blue gate in "c". Install orange head in "M", blue head in "E", purple head in "F"
This will open a door on the golden putter with two heads.
6-gate-sequence: Install purple gate in "j", yellow gate in "k", red gate in "f", blue gate in "c", green gate in "b". Install purple head in "M", orange head in "D", blue head in "I", red head in "J", purple head in "F"

Fix the plumbing in the garden.
In The green house, you'll find both a diagram and a "Maintenance note" pinned to it. This is all the information you need, but not all the tools.
You'll need two big metal wheels to fix two disassembled valves. The first one can be found behind the gardeners house. To release it, you'll need the hammer that lies on the garages windowsill, obtainable from the outside. The other big metal wheel is past the excalibur sword and the red way back to the starting shore. You'll need the padlock key, found in the garage above the bikes, to release that one.
Once you have the wheels and the info, let's get to work. According to the maintenance note, D always goes to G no mattes which way you turn it, H needs to be included as it has a filter, A and E are not connected (blocked pipe), F and H are not connected (no pipe at all), A and B are 180° wrong.
Not stated, but A is the source of the water.
This leaves us with this:

The red lines are clogged/non existent pipes. The blue line is what we want.
Set all the wheels according to the blue line, with the building in the middle as a reference point (the half circle is the entrance door, the front of the mansion points rightwards) making sure A and B point opposite where they ought to go, and the achievement will pop.
Facing the mansion, that means A forwards, D any direction, G backwards, C to the left, B backwards, F to the left, E to the left, (still facing mansion but now from behind) H to the left, K to the left.

Cook and serve the dinner.
Collect the ingredients for the soup of the decade:
Carrots - Gardener living room
Beans, tomato juice - chef's room, in cans
Potato - Basement, on table
Chilled cheese - White fridge in kitchen (open green, red, blue, yellow fridges in order)
Salt - Kitchen storage (locked cabinet, hint is on the wall of the kitchen, around the corner from storage entrance, position the ladders like on the meal menu)
Dice everything on the kitchen counter. Fetch the pan from the counter, fill it with water with the only faucet that can do that (the one below the soup-of-the-decade chalkboard), put it on the stove and start the stove using the button inside the oven. Put all ingredients in, fetch the soup and put it on the dinner table.

Solve the picnic mystery.
In the chef's room is a "Knife to meat you" poster. The knifes are numbered, and oh, there are knife boards on the wall with a weird assortment of knifes.
Use those knife boards to get 4 codes of different length.

The codes

2897, 11959, 228567 and 2885675

.
Out in the garden are 4 picnic baskets which have differing amounts of digits needed to unlock. One is in the gazebo left of the house, one is a bit further where the excalibur sword and red gate to the shore is, one is on the badminton court and the last one is in front of the gardeners house.
Collect the safe knobs from all of them and return to the chefs room. Assemble all the knobs (and the safe handles if you haven't, they're all in the room), then look at the ceiling for the save code.

Solution

Middle knob up, then from the top knob counter-clockwise lower left, lower right, upper right, left.

Dress up the mannequins.
There are two mannequins to dress.
One is in the fashion show in the labyrinth center. As this one is a must for progression to the house, I'll skip the description here (in short: dress the mannequin on stage with the hairpin, belt, umbrella and fan that are on the mannequins you can't take them from and on the roof). The second mannequin is in the workshop.
Gather all the hats you can find (pink one is in the cabinet behind boxes as you enter the workshop, white one is on the chair right next to it, blue one in the briefcase on the long table, purple one in the workshop storage on the windowsill, yellow one right next to it). Gather all the shoes you can find (all in workshop storage, yellow pair in the shelf as you enter, red dead ahead opposite door, black right next to the windowsill where the purple hat was, beige in cabinet below painting and unobtainable blue shoes)
Solve the mirror puzzle boxes in the courtyard and on the workshop balcony to gain two hints and two keys.
Puzzle box solutions (click on image to get full size):



Use the keys to open the two locked shelves in the workshop.
Dress up the mannequin using the hints from the puzzle boxes (the correct cloth is in the box), high on and on the workshop wall left of it and in the window frame of the workshop storage.

Become a botanical mastermind.
Go to the gardener's bedroom and look at the wall poster to find out about roman numerals: I = 1, V = 5, X = 10, C = 100, D = 500, M = 1000 (and this game's special version, a V with a line over it = 5000). As with real life roman numerals, a smaller numeral in front of a bigger one means the bigger one minus the smaller one. CM is 900 (1000 - 100) while MC is 1100 (1000 + 100), for example.
Other hints are in "Secret Codes 1.0" and "Secret Codes 1.1". Forgot where they are but I think in the gardeners house and garage respectively - write a comment if you know.
From secret codes 1.0, we learn that each column of buttons stands for one digit, top button is 4, middle button is 2, lower button is 1.
From secret codes 1.1, we learn that numbers larger than 7 (1+2+4) are put in by first having all buttons in a column pressed (7) and then pressing the button for 1 or 2 in the next column. So 972 and 7272 and 99 results in the same buttons.
Using this knowledge, go open all 5 plant boxes in the garden. All but one have roman numerals on them, some times quite well hidden, the last one, next to entrance from the labyrinth with a pin on top, has the solution on the tree next to it.
Bring those plants back to the gardeners house and place them on the "scales" in his living rooms to find out what they stand for. Knowing this, read the note you found in the gardeners house, "Gardeners Poem". It tells you how to arrange the plants on the scales.

The orderm knowing what each plant stands for

Apple, carrot, cabbage, corn, grapes -> plant with small round leaves, plant with big leaves, plant with white flowers, plant with long pointy leaves, plant with red flowers

This will open the compartment, getting you the plant name plaques.
Leave the house and go to the vegetable garden in front of it. 2 plant pots have seed packets on them making it easy for you, the rest you must determine by the text on the plaques.

The correct order for the plaques

Clockwise order from entry door: Basil, Bay Laurel, Chives, (Coriander), Parsley, (Lemon Balm), Oregano, Peppermint, Thyme, Sage

Find out what the Admiral is hiding.
Find the cryptic sign for the cabinet in the Admiral's study (there are two, one between the shelves which you'll want, one between the lounger and the wall) and install it on the cabinet (-> open project). Type that code (openproject) using the typewriter, revealing the Project: Project wall.
Read the Project: Project signs and then go to answer the three questionnaires, one in the study, one on the study balcony and one in the master bedroom.

Answers

Project Mars (study): Confectionery, not enough data, false, false.
Project Pluto (balcony): Sweets + seeing others in distress, (all 3), (none), Venus + Pluto
Project Venus (master bedroom): 0.026.. hours, false, Venus, (none)

This will cause a direction to highlight on all questionnaires, N for Pluto and Venus, W for Mars. It will also open the cabinet where you installed the sign. Open it.
Inside are three busts, labeled Venus, Mars and Pluto. On the cabinet door are also three arrows. All busts have two buttons, one which changes the position and one which turns them.
Have them all in the position of the arrows and facing the direction highlighted on their quiz boards. Which direction is north can be determined by the compass that is in the drawer of the table in the master bedroom.

Solution

North is to the right of the drawer. Have Venus on the left facing right, have Mars on the right facing away from you, have Pluto on the right facing right.

Get ready for dinner.
First collect all the ingredients for setting a dinner table: Plates, Napkins and Figurines.
Plates: Green one is on the wagon in dining room, beige one in the kitchen counter opposite the door, red one is above pans on kitchen wall, black one is in the oven, blue one is in kitchen sink.
Figurines: Giraffe is in the middle left drawer of the makeup table in Amelia's room, Unicorn is in Bella's room under the phone, Spider is in Della's room on the purple table, Fox is in the workshop storage at the window, Stag is in master bathroom on the sink.
Napkins: All 5 napkins are strewn about in the butler's room.
Now get the dinner rules from the locked cabinet in the dining room. The code is in the butler's room. 4 numbers on his to do list are circled (6,7, 8, 9) and the to do list contains a note "rules (arrow up)", so the code is 9876.
The rules determine where each item goes. You can cheat with the figurines if you remember where you found them. If you're anything like me and would have forgotten that if you didn't take notes for steam guide, don't fret, the dinner rules don't rely on that knowledge.

Correct placement

Head of the table: Stag, pink napkin, green plate. Right of the table (with a single seat able to set): Giraffe, blue napkin, blue plate. Left of the table bottom (leftmost): Unicorn, green napkin, red plate. Left of the table middle: Fox, red napkin, beige plate. Left of the table top (rightmost): Spider, beige napkin, black plate.

Sort out the library.
Collect the chess game notes "Note regarding chess" (on table with chess board), Note about chess (On chair of upper floor), Excerpt from Strange chess rules (in lower library door).
Collect all the 6 chess pieces in the library (and all the 5 books while you're at it), the highlight-items-button is your friend yet again.
Solve the chess board withe Amelia's special rules.

Solution

Top to bottom, left to right: Queen, bishop, knight, pawn, king, rook.

This reveals "A note about chess lectures" in which the admiral tells us he prepared a puzzle wall in which you have to input all possible moves according to Amelia's rules one step further. This is the big checkered wall.
Now, personally I'm still somewhat sure that is not according to the rules, as some seem to need at last two movements because some pieces are set in place in relation to each other and not free to move in a single play, but the correct solution is this:

After this, flip the switch next to the puzzle.
This opens the diagram on the upper floor:

The bookshelves on this are swapped vertically (the upper ones are on the lower floor) but left to right they're accurate. The middle at the bottom looks wrong because the top right in the drawing has a gap and the shelf itself has no gap there - this is probably a bug, it is the middle shelf.
The books you found have numbers on them. The side the numbers are on doesn't matter, all are valid. All but one of the books only have a single place where they could fit according to the diagram, and the remaining one is set because another book with just one possible place takes up one of the two possibilities.

Solution

Blue 4: Old Christmas. Red 6: Sonnets of three centvries. Yellow 3: The Blue Bird. Red 1: Folk Tales From Many Lands. Green 5: Poems and Songs of Fairyland. Green 2: The Vicar of Wakefield.

Put the perfumes to good use.
First you need all 9 perfumes. They are hidden inside the sisters rooms, many hidden behind small puzzles.
You know from the other achievements that I would detail where to find each - if I noted it down, which I did not. So, well, good luck :D
Once you have all 9, go to the big cabinet in Amelia's room and open it. You're faced with a puzzle and 3 empty perfume spots.
The puzzle needs not much more info, but the perfume spots are determined by the animals in the puzzle and the animals associated with the perfumes (open inventory and look at the perfume bottles, each has an animal printed on it). The order is determined by three hints hidden around the rooms. One, for the first puzzle, is in the top right drawer of Amelia's makeup table, the one for the second puzzle is on the wall to the right of the cabinet, around the corner, the last one is in Della's bathroom, next to the sink.
Once you solve this first puzzle, it will continue in the same vein 2 more times, so allow me to concatenate:

First puzzle solution

You'll need to click bottom left 2 times, top right 2 times, top left one time and bottom left one time. The perfume order is bear - fox - squirrel.

Second puzzle solution

You'll need to click top left 2 times, bottom left one time, top right 2 times, top left one time. The perfume order is eagle - kangaroo - frog.

Third puzzle solution

The click puzzle doesn't actually matter, just place the perfumes, but for completeness' sake, you'll need to click bottom right 3 times, top left one time, bottom right one time, top right one time, bottom right one time, top left two times, top right two times, bottom right one time, top left 5 times, top right 2 times and once on bottom right. The perfume order is elephant - crocodile - lion.

Find Amelia’s treasure.
Go to Amelia's room and find 3 treasure maps.
The first one is in her wardrobe next to the bed - be sure to also pick up the slab. The second one is in the mask cabinet. The third one is in her secret hiding place, see "I Spy" achievement on how to open it. The only one that matters for the achievement is the third one, but let's be thorough.

All three are digging spots, you need the shovel from the garage for them. The first two will reveal slabs and aren't really necessary for the achievement, they're on weirdly colored ground on the western shore, one about in the middle of the way down and the horseshoe one-armed-bandit, one shortly before the tree outcropping in front of the lighthouse.
The third one, to the right of where you started the whole game (ignoring tutorial) will reveal a huge puzzle box.
This alone unlocks the achievement, but for completeness' sake, let's continue:
First step is the signs on the corners. For each row, one sign will be red and fixed, just turn the rest to fit the first. This will lower the outermost walls. Now you have two walls you can't interact with and two walls opposite them where you can. Turn the symbols on a wall where you can turn and the symbols opposite (that you can't manually interact with) turn as well. Turn each symbol so the opposite wall is all right side up. This will expand the box. Climb on top of it and insert the slabs (one from Amelia's wardrobe, the two you dug up and the one lying to the side of the very console you stand in front of). Turn the knob so it's still on yellow and points to the right, the right side of the puzzle will light up. Turn each symbol that has an arrow pointed at it. Advance the knob on top one space and turn once and do the same with the now light up side, repeat 2 more times.

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