Here is the full list of all 58 Day of the Tentacle Remastered achievements. It takes around 3-4 hours to unlock all of the achievements on Windows.
Get all other achievements in the game
Cook the hamster in Maniac Mansion (Don't try this at home, kids!)
Reach yesterday without turning the stereo off
Talk to Washington, Jefferson, or Hancock while they're outside
Laverne thinks about eating the cat
Ring the front desk bell 100 times
Try to sign the contract yourself with the quill pen
Flush 50 objects through time
Laverne tries the chattering teeth on her human during the human show
Try to swap the textbook with the stamp album
Hoagie uses battery with Chron-o-John instead of plug
Try to mix the red paint and the Booboo-B-Gone
Squirt five different people with disappearing ink
Try to wash the dirty car with the brush
Try to alter the contract with Booboo-B-Gone
Try to microwave the hamster again after he's thawed out
Try to mix the disappearing ink with Booboo-B-Gone
Try to put something metal in the microwave
Try to mix the decaf and caffeinated coffees
Talk to Dead Cousin Ted with all three kids
Turn off the television
Try to flush the hamster
Sit through the end credits
Ask the IRS agents if they're related
Play the whole game without skipping a cutscene
Return the stamp album to Weird Ed
Defeat Purple Tentacle yesterday
Vacuum up a hamster
Power Laverne's Chron-o-John
Acquire a diamond
Pick up 45 things that don't belong to you
Get Fred to sign the contract
Power Hoagie's Chron-o-John
Win the human contest
Get a tiny sweater
Disqualify Harold
Make a skunk
Wake up Dr. Fred
Red makes a super battery with only a little help from Hoagie
Microwave the frozen hamster
Enter the human contest
Climb through the chimney with all three kids
Make vinegar
Deflate Oozo
Get a job
Get all six novelty items
Clothe Laverne in the costume
Hoagie eats a Hoagie
Change the flag
Play Maniac Mansion
Pick up 30 things that don't belong to you
Make it rain
Open the safe
Destroy a cherry tree
Create a cherry tree
Pick up 15 things that don't belong to you
Close a door
Find Fred's basement workshop