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.
Sit through the end credits
Play the whole game without skipping a cutscene
Defeat Purple Tentacle yesterday
Power Hoagie's Chron-o-John
Power Laverne's Chron-o-John
Vacuum up a hamster
Acquire a diamond
Turn off the television
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
Open the safe
Hoagie uses battery with Chron-o-John instead of plug
Get a job
Make it rain
Red makes a super battery with only a little help from Hoagie
Make vinegar
Get all six novelty items
Microwave the frozen hamster
Get a tiny sweater
Pick up 30 things that don't belong to you
Close a door
Make a skunk
Win the human contest
Disqualify Harold
Deflate Oozo
Enter the human contest
Clothe Laverne in the costume
Change the flag
Pick up 15 things that don't belong to you
Destroy a cherry tree
Create a cherry tree
Find Fred's basement workshop
Get all other achievements in the game
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
Try to microwave the hamster again after he's thawed out
Hoagie eats a Hoagie
Reach yesterday without turning the stereo off
Play Maniac Mansion
Ask the IRS agents if they're related
Talk to Dead Cousin Ted with all three kids
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 flush the hamster
Try to swap the textbook with the stamp album
Laverne thinks about eating the cat
Try to put something metal in the microwave
Ring the front desk bell 100 times
Cook the hamster in Maniac Mansion (Don't try this at home, kids!)