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