Here is the full list of all 48 Crash Team Racing Nitro-Fueled trophies - there are 35 bronze, 10 silver, 2 gold and 1 platinum.
Finish first on all tracks. (CTR & CNK)
Use all of Blizzard Bluff's shortcuts in the same race.
Earn all the shortcut trophies.
Use every Power-Up once. (Race & Battle Arena)
Use the shortcut in Cortex Castle.
Use the shortcut in Dragon Mines without being crushed.
Use all of Papu's Pyramid's shortcuts in the same race.
Win a Cup Race in the Adventure Mode.
Win against Nitros Oxide in the Adventure Mode.
Win against PinStripe in the Adventure Mode.
Drift 15 Times in a row during a race.
Win against Komodo Joe in the Adventure Mode.
Use the shortcut in Polar Pass.
Drift Boost a total of 500 times.
Use the shortcut in Sewer Speedway.
Win against Papu Papu in the Adventure Mode.
Use the shortcut in Tiger Temple.
Complete a Crystal Challenge in the Adventure Mode.
Win a Relic Race in the Adventure Mode.
Win a CTR challenge in the Adventure Mode.
Use the shortcut in Crash Cove.
Hit two opponents with a single Bowling Bomb.
Win a race with less than 0.3 seconds between you and the second place.
Finish first when you were last on the final lap.
Do a Super Boost.
Win a race without using any Power-Ups.
Win against Ripper Roo in the Adventure Mode.
Win a boss challenge without getting hit by any of the boss' Power-Ups.
Successfully land all three missiles from a Triple Missile Power-Up.
Win your first race in the Adventure Mode.
Free yourself from a TNT crate.
Customize your ride.
Earn all the other trophies.
Defeat Nitros Oxide in the Adventure Mode once and for all.
Earn all the Relics in the Adventure Mode.
Earn all the Gems in the Adventure Mode.
Earn all the CTR Tokens in the Adventure Mode.
Successfully use all three Turbo Boost charges 5 times in a row during a race.
Complete the Adventure Mode on the Hard difficulty.
Block an incoming missile with all of the following Power-Ups: Beaker, Crate, Bowling Bomb.
Beat all of Nefarious Tropy's times in Time Trial Mode.
Beat all of Nitros Oxide's times in Time Trial Mode.
Use all Juiced Up Power-Ups once. (Race & Battle Arena)
Sustain your boost for a whole lap.
Win a match in every type of Battle Mode.
Directly hit an opponent with a thrown Beaker Power-Up.
Unlock all characters from the original roster.
Complete all Crystal Challenges. (CTR & CNK)