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