Hints
Episode I: It's About Time Trophies
There are 7 bronze, 4 silver, and 1 gold trophy to collect.
A Bicycle Built for Two (Gold): Rescued Doc from Kid Tannen
A Plausible Explanation (Bronze): Discovered the origin of the "new" DeLorean
Back in Time (Silver): Traveled back in time to rescue Doc
Deja Marty (Bronze): Perfectly repeated dialog while repeating Doc's temporal experiment
Doc's Legacy (Bronze): Got Doc's Notebook back from Biff
Fate in flux (Bronze): Heard about the curious fate of Marshall Strickland
Fuelmaster (Bronze): Flawlessly mixed up a batch of Emmett's Rocket Fuel
Grandpa Got Served (Silver): Delivered the subpoeana to Arthur McFly
Hello, Young Friend (Bronze): Talked Emmett into completing the Rocket Drill
Hi Bob! (Bronze): Namechecked BTTF Creators
Jailbreak! (Silver): Acquired Emmett's Rocket Drill
Junior Bootlegger Badge (Silver): Managed to get 190-proof alcohol delivered to Emmett's

Episode II: Get Tannen! Trophies
Complete each requirement to get the specified Trophy. There are 6 Bronze Trophies, 4 Silver Trophies and 1 Gold Trophy.
A Minimum of Panic (Bronze): Rescue Arthur with minimal fuss.
Art Lover (Bronze): Track down a missing accountant.
Chucklehead (Bronze): Find "Chuckles Lenart".
Demystifier (Bronze): Get a full explanation of your situation.
Door Prize (Bronze): Break the password code without cheating.
Escape Artist (Silver): Find a hidden passageway.
Kid Restraint (Gold): Defeat Kid Tannen
Moll Mender (Silver): Get a gangster's girl to do the right thing.
Police Blotter (Silver): Dry a cop out.
Tannen Tamer (Silver): Defeat the Tannen Brothers in six jumps.
Tuned Out (Bronze): Enjoy a full set from Hill Valley's leading songstress.

Episode III: Citizen Brown Trophies
All Good Dogs Go To Utah (Silver): Got caught with Einstein
Final Solution (Gold): Layout Biff and escape the speakeasy.
Hidden Treasure (Bronze): Examine every container of contraband in the speakeasy
Hill Valley Tourist (Bronze): Listen to all tourist audio guides in Hill Valley
Hope You're Insured (Silver): Use the DeLorean parts to enter Hill Valley
Intervention (Silver): Got caught with Lorraine's booze
Into the Garbage Chute, McFly-boy (Silver): Jumped the Decycling Bin
Marty and the Pinheads (Bronze): Use the spray can to paint Marty's band name in the alley
One Bad Apple (Bronze): Collect every Demerit in the game
Ruin it for Everyone (Bronze): Coax Edna out of the courthouse with the buzzer
Seven Minutes in Heaven (Silver): Got caught making out with Jennifer

Episode IV: Double Visions Trophies
Complete each requirement to get the specified Trophy. There are 9 Bronze Trophies, 3 Silver Trophies and 1 Gold Trophy.
A Not-So-Beautiful Mind (Bronze): Crafted a Mind Map of Emmett that Reveals him to be a "Degenerate Criminal."
An Uncomfortable Truth (Bronze): Emmett is Prophetically Honest About His Marriage Prospects.
Breaking Up is Hard to Do (Silver): Broke up Emmett and Edna.
Edna Was Right! (Bronze): Revealed Hill Valley Hooliganism Rate
Free Citizen Brown! (Silver): Rescued Citizen Brown from the Citizen Plus Program.
Let Them Eat, Um, Cake (Bronze): Offered Algae Cakes to Everyone
Like a Not-So-Fine Wine (Bronze): Messed with Emmett's Cleanser.
The Other Woman (Bronze): Got Trixie Ready to Make Edna Jealous
The Power of Love? (Bronze): Escaped from Marty's Cell.
There's a Moose? (Bronze): Get a Good Look at Trixie's Postcard
Timely Traveller (Bronze): Take the Fewest Possible Trips to Emmett's Lab
To the Expo! (Gold): Marty and Emmett head to the Expo.
Your Own Personal Frankenstein (Silver): Gave Emmett his Epiphany.