Keen Mind
As the hint suggests, just underline the word "Arkhamend" in the letter left for you at the start of the game.

Sweep the floor
Search the ceiling of the top floor at the start of the game. You'll find a hidden attic access panel. Open it and enter to unlock the achievement.

Unlock the Secrets Inside
Should unlock automatically as you progress through the first dream sequence in the hotel.

Bygone Days Telling Tales
Should unlock automatically at the end of the first dream sequence.

Smooth Talker
Should unlock automatically after you persuade Henry to sell you the book you were sent to find.

Seeker of the things that should not be
Carefully search the basement of Henry's bookstore. Crouch down and inspect the floor under a crate near the entrance. You may need to push or jump onto the crate to find what you're looking for. After you discover a hidden panel, you can pull the crate aside and open it. The achievement will unlock as you inspect the contents.

In Remembrance
Achieved by successfully solving the book lock puzzle.

Meadow Mystery
Should unlock automatically as you begin to make your way to the old building for the first time.

Piece it Together
Unlocks after solving the circle puzzle in the old building AND finding a way to secure the pieces together.

No Stone Unturned
Should unlock automatically after taking the key hidden in the dining room of the old building.

Going Down
Should unlock automatically after solving the elevator combination puzzle.

Hidden Room
Get bitten by insects enough to begin to hallucinate. You will hear a message repeating in Morse code in some parts of the underground (near the body worked for me). Translate the Morse code into letters. This message will be the door code to the "hidden room." Unlock the door and enter to activate the achievement.

Bug Killer
Unlocks automatically after you spray the insects off the cabinet.

Cover Up
Achieved by solving the locked closet puzzle with the three sticks. The sticks themselves are found in the left cupboard covered with insects down below in the old building. Collect all three (one at a time) and use each on the locked closet upstairs, in the first bedroom. Then you must solve a short puzzle in which you line up all the three sticks on the line where the unpainted region touches the painted region. Once finished, the closet unlocks. Open it and take the suit to complete the achievement.

Making a new friend
Complete the "Hidden Room" achievement. Unlock the metallic box inside with the "Strange Shaped Key" found in the area below the old building. Taking the contents should unlock the achievement.

Necromancer
Unlocks automatically after you complete the process of summoning Wolfgang Schneider using the machine underground.

Pull back the Vale
Unlocks automatically as you first visit "The Gate."

Down in the Dumps
Unlocks automatically after you gain entrance to the cellar of "The Gate."

Toys and Tools do Mix
Find the ankh in the chest in the cellar of "The Gate." (Note: the name seems to be a reference to how you found the ankh in previous versions of the game.)

Flashlight Collector
Collect all four flashlights hidden throughout the game. One is in the bedstand next to you in the house where you first wake up, one is in your hotel room bedstand, one is inside near the entrance of the old building, and one is in the drawers in the living room of "The Gate."

Childhood Trauma
Unlocks automatically after completing the first dream sequence at "The Gate."

Keep Looking Down
Find and open a hidden compartment in the floor of your grandfather's library at "The Gate." The achievement should unlock as you collect the contents.

Gotta hand it to you
Find the hairpin in the bathtub off the master bedroom in "The Gate." Take it downstairs to the room with the fireplace. There, you'll find a cabinet containing a locked box. Use the hairpin to pick the lock. The achievement should unlock as you examine the contents.

Family Reunion
Unlocks automatically after finding your father's coffin in the tomb.

Long Awaited Reunion
Unlocks automatically after speaking to Loath Nolder.

Search high and low
After smashing the cellar floor with the mallet, enter the room with the insects below. Put on the insect suit collected at the old building. Approach the table while wearing it and take the small key amongst the insects, on the left. Later, use this key to unlock the door in the kitchen. The achievement should unlock after you enter.

Statuesque Secret
Early in the game, purchase the music box from Henry. Later, do everything required to unlock the "Search High and Low" achievement. In that same room off the kitchen, stand just in front of the three busts grouped together. Open the music box and play it. A small scene should play, after which the achievement will unlock.

Bookshelf Bonus
As soon as you return to town from "The Gate," head back to Henry's bookstore. Examine the book on his store counter. The achievement should unlock.

Grim Discovery
Complete the "Making a new friend" achievement. Later, just after returning to town from "The Gate" for the first time, head back to Henry's bookstore. Henry will not be there. Head down into his cellar. A cutscene should activate and reveal a hidden door. Enter the new area to unlock the achievement.

Second Piece
Unlocks automatically after solving the alarm puzzle and taking the second piece in the lower level of the old nursing home.

No Outsiders Here
Complete the "Making a new friend" achievement. Later, after returning from the sewers, go back to the hotel. The innkeeper will not be around. Take both keys, and search the second floor room you can now unlock. A cutscene should play, followed by the unlocking of the achievement.

Last Piece
Find the third piece of the key inside the hotel room where your grandmother stayed.

Master Detective
Complete the "Search High and Low" achievement. Later, after returning to the mansion with all three piece of the key, return to the secret room off the kitchen. You will find a new item on the desk. Examine it to unlock the achievement.

Lord of the Secrets
After returning to the mansion with all three piece of the key, go back into your grandfather's library. On his desk, you will find two new books. Examine both to unlock the achievement.

Into the Darkness
Unlocks automatically after solving the elevator steam valve puzzle.

Last leap into Unknown
Unlocks automatically after you use the key on the door in the Necropolis.

Lesser of Two Evils
Unlocks automatically if you end the game by stabbing the crystal, assuming you do NOT have your family ring in your inventory. (If you do have it, you get "Pessimist" instead.)

Pessimist
Complete the "Search High and Low" achievement. In the same secret room off the kitchen, one of the statues is wearing your family ring. Find and take it. Then, during the endgame sequence, tell the crystal god "Yes, I have to walk the path my ancestors travelled before me." Finally, stab the crystal.