Here is the full list of all 58 Day of the Tentacle Remastered trophies - there are 53 bronze, 3 silver, 1 gold and 1 platinum.
Get all other trophies in the game
Flush 50 objects through time
Try to microwave the hamster again after he's thawed out
Sit through the end credits
Play the whole game without skipping a cutscene
Defeat Purple Tentacle yesterday
Reach yesterday without turning the stereo off
Power Hoagie's Chron-o-John
Hoagie uses battery with Chron-o-John instead of plug
Power Laverne's Chron-o-John
Vacuum up a hamster
Microwave the frozen hamster
Laverne thinks about eating the cat
Pick up 45 things that don't belong to you
Make a skunk
Laverne tries the chattering teeth on her human during the human show
Try to sign the contract yourself with the quill pen
Try to alter the contract with Booboo-B-Gone
Red makes a super battery with only a little help from Hoagie
Acquire a diamond
Try to flush the hamster
Win the human contest
Disqualify Harold
Enter the human contest
Talk to Dead Cousin Ted with all three kids
Make vinegar
Get a tiny sweater
Clothe Laverne in the costume
Climb through the chimney with all three kids
Change the flag
Deflate Oozo
Get Fred to sign the contract
Open the safe
Wake up Dr. Fred
Talk to Washington, Jefferson, or Hancock while they're outside
Ask the IRS agents if they're related
Pick up 30 things that don't belong to you
Turn off the television
Squirt five different people with disappearing ink
Try to swap the textbook with the stamp album
Try to mix the red paint and the Booboo-B-Gone
Try to put something metal in the microwave
Try to wash the dirty car with the brush
Try to mix the decaf and caffeinated coffees
Try to mix the disappearing ink with Booboo-B-Gone
Cook the hamster in Maniac Mansion (Don't try this at home, kids!)
Get a job
Ring the front desk bell 100 times
Get all six novelty items
Play Maniac Mansion
Return the stamp album to Weird Ed
Close a door
Pick up 15 things that don't belong to you
Destroy a cherry tree
Create a cherry tree
Make it rain
Hoagie eats a Hoagie
Find Fred's basement workshop