If you perform certain tasks in the game, you'll unlock special trophies that can be viewed in The Secret Lab.

Trophy	How to unlock
Fifth Super Gravitron Trophy	Last 30 seconds on the Super Gravitron.
Final Level Mastered	Obtain a V Rank in the Final Level Time Trial.
First Death Trophy	Win with less than 500 deaths.
First Super Gravitron Trophy	Last 5 seconds on the Super Gravitron.
Flip Mode Complete	Beat Flip Mode.
Fourth Death Trophy	Win with less than 50 deaths.
Fourth Super Gravitron Trophy	Last 20 seconds on the Super Gravitron.
Game Complete	Beat the game.
Laboratory Mastered	Obtain a V Rank in the Laboratory Time Trial.
Master of the Universe	Complete No Death Mode.
Second Death Trophy	Win with less than 250 deaths.
Second Super Gravitron Trophy	Last 10 seconds on the Super Gravitron.
Sixth Super Gravitron Trophy	Last 1 minute on the Super Gravitron.
Space Station 1 Mastered	Obtain a V Rank in the Space Station 1 Time Trial.
Space Station 2 Mastered	Obtain a V Rank in the Space Station 2 Time Trial.
The Tower Mastered	Obtain a V Rank in the Tower Time Trial.
Third Death Trophy	Win with less than 100 deaths.
Third Super Gravitron Trophy	Last 15 seconds on the Super Gravitron.
Warp Zone Mastered	Obtain a V Rank in the Warp Zone Time Trial.