To unlock character specific icons and titles you must clear Arcade mode under certain circumstances and complete each unique character's set of trials.

Unlockable	How to Unlock
Blue Character Title	Clear Arcade with the character on any difficulty.
Character Icon #1	Complete any trial with the character.
Character Icon #2	Complete 8 different trials with the character.
Character Icon #3	Complete 16 different trials with the character.
Character Icon #4	Complete all trials with the character.
Gold Character Title #1	Complete 12 different trials with the character.
Gold Character Title #2	Complete 14 different trials with the character.
Gold Character Title #3	Complete 18 different trials with the character.
Gold Character Title #4	Complete 20 different trials with the character.
Gold Character Title #5	Complete 22 different trials with the character.
Red Character Title	Clear Arcade with the character on the hardest difficulty.
Silver Character Title #1	Complete 2 different trials with the character.
Silver Character Title #2	Complete 3 different trials with the character.
Silver Character Title #3	Complete 4 different trials with the character.
Silver Character Title #4	Complete 6 different trials with the character.
Silver Character Title #5	Complete 10 different trials with the character.