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