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