In the cut scene before fighting Liz there's an option appears that says "Find a path for Yuuto",if you select this you'll be unlocking Stage 3-B ,at the end of the level You'll find The cop chief.

After beating Stage 3-B you unlock the rookie magician beat the game with her all the way thru stage one and you'll get the achievement

1CC Run Hype

Shoutouts to a single flipper

if you play with the Chizuru: you can spam right click and gain speed out of anywhere,also if you want to melt bosses health quickly don't forget to stock up on Fire bullets and spam it as soon as possible

If you play with Bootleg Magician:Even though I didn't find the playability quite well on this character I managed to beat the game under 10 minutes with her and didn't die.
In bosses try to freeze enemies with ice and then spam fire or just try to use spread when you freeze the enemy
You can quite spam the rocket to fast travel by pressing space,this character doesn't have a dodge or absorb option so use the rocket as a dodge mechanic and fast travel option.Rocket doesn't even consume that much mana but be careful on bosses because your bullets needs mana to shoot out as well.