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