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