Unlock puzzles:

Hard mode puzzles:
     Successfully complete all puzzles in normal mode.

Special mode puzzles:
     Successfully complete all puzzles in hard mode.

Mania mode puzzles:
     Successfully complete all puzzles in special mode.

Unlock Chao in the game:
     Beat  all 25 levels in Stage Challenge Mode to have the Chao from
Sonic Adventure replace the Mice.

Unlock NiGHTopians in Puzzle mode:
     Complete all 25 Mania puzzles