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