Ghost Sweeper Mikami

Goal: Clear Report 4
Start: Title Screen
.done: CLEAR, followed by REPORT 4 appears.
Controls:
B - Jumps
Y - Attacks
X - Special Attack (limited)
Up + Y - Different attack that can grab hooks, press up again to climb

The levels have checkpoints, and the game has unlimited continues which start you at the beginning of the stage you game overed on.

Using special weapons can grant invincibility frames, which can make some sections easier, or just give you a moment to chill out.