https://youtu.be/y32f574nWCI
00:00 Sanctar easy
00:28 Sanctar hard
01:24 Foliana easy
01:59 Foliana hard
02:52 Balnea easy
03:22 Balnea hard
04:24 Ambrose easy
04:57 Ambrose hard
06:01 Park easy
06:30 Park hard
07:30 Transidor easy
07:58 Transidor hard
09:04 Costumes

Just some personal bests, these are FAR from optimized runs.

This whole mode is entirely optional and I'm pretty sure you only need Gold medals to unlock all costumes (which is much easier to do). Platinums require some more skill to obtain.

UPD: one of the costumes might require Platinums.