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