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