Level select
Press Start to pause the game, then press Square, Circle, Triangle + Square, Square, Circle, Start.

Pass through objects
Press Start to pause the game, then press Square, Circle, Square + Circle, Square, Circle, Start.

Oscar
Finish the game with an "A" rank in every level.

The Insider
Finish the Storage level with a "B" rank.

J. J. Sawyer
Finish the game with an "S" rank in every level.

Naomi
Finish the Downtown level with a "B" rank.

Stunt attack mode
Finish the game in story mode.

Different costumes
Finish one of the tasks below to unlock a third costume for the mentioned character.

Ethan costume C: Finish stunt attack mode.
Kat costume C: Finish score attack mode with high scores in all levels.

Corporate HQ: Stop on cable car
Select Ethan and go into stunt mode. Then play the Corporate HQ level and go to the last cable car. When you are grinding it, press R1 and you will stop on it.