Here is the full list of all 58 Day of the Tentacle Remastered achievements. It takes around 5-6 hours to unlock all of the achievements on Windows.
Get all other achievements in the game
Reach yesterday without turning the stereo off
Try to sign the contract yourself with the quill pen
Talk to Washington, Jefferson, or Hancock while they're outside
Try to alter the contract with Booboo-B-Gone
Laverne tries the chattering teeth on her human during the human show
Cook the hamster in Maniac Mansion (Don't try this at home, kids!)
Turn off the television
Try to mix the red paint and the Booboo-B-Gone
Try to mix the disappearing ink with Booboo-B-Gone
Sit through the end credits
Play the whole game without skipping a cutscene
Defeat Purple Tentacle yesterday
Power Hoagie's Chron-o-John
Acquire a diamond
Flush 50 objects through time
Get Fred to sign the contract
Wake up Dr. Fred
Power Laverne's Chron-o-John
Vacuum up a hamster
Win the human contest
Ask the IRS agents if they're related
Open the safe
Pick up 45 things that don't belong to you
Disqualify Harold
Get a tiny sweater
Laverne thinks about eating the cat
Make a skunk
Try to wash the dirty car with the brush
Hoagie eats a Hoagie
Try to microwave the hamster again after he's thawed out
Microwave the frozen hamster
Enter the human contest
Squirt five different people with disappearing ink
Hoagie uses battery with Chron-o-John instead of plug
Red makes a super battery with only a little help from Hoagie
Make vinegar
Get a job
Talk to Dead Cousin Ted with all three kids
Clothe Laverne in the costume
Try to put something metal in the microwave
Get all six novelty items
Try to swap the textbook with the stamp album
Change the flag
Climb through the chimney with all three kids
Pick up 30 things that don't belong to you
Make it rain
Ring the front desk bell 100 times
Deflate Oozo
Destroy a cherry tree
Create a cherry tree
Return the stamp album to Weird Ed
Pick up 15 things that don't belong to you
Close a door
Try to flush the hamster
Try to mix the decaf and caffeinated coffees
Play Maniac Mansion
Find Fred's basement workshop