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.
Defeat Purple Tentacle yesterday
Play the whole game without skipping a cutscene
Sit through the end credits
Acquire a diamond
Get Fred to sign the contract
Power Hoagie's Chron-o-John
Red makes a super battery with only a little help from Hoagie
Power Laverne's Chron-o-John
Vacuum up a hamster
Get all six novelty items
Pick up 45 things that don't belong to you
Win the human contest
Deflate Oozo
Wake up Dr. Fred
Laverne tries the chattering teeth on her human during the human show
Make a skunk
Try to flush the hamster
Disqualify Harold
Make vinegar
Enter the human contest
Microwave the frozen hamster
Talk to Dead Cousin Ted with all three kids
Clothe Laverne in the costume
Ask the IRS agents if they're related
Change the flag
Climb through the chimney with all three kids
Get a tiny sweater
Get a job
Hoagie eats a Hoagie
Try to sign the contract yourself with the quill pen
Return the stamp album to Weird Ed
Pick up 30 things that don't belong to you
Make it rain
Try to alter the contract with Booboo-B-Gone
Open the safe
Destroy a cherry tree
Create a cherry tree
Pick up 15 things that don't belong to you
Play Maniac Mansion
Close a door
Turn off the television
Find Fred's basement workshop
Get all other achievements in the game
Flush 50 objects through time
Try to wash the dirty car with the brush
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
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
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!)