For context in the mission, you have to defeat Satsuki with an Instant Kill because she has no healthbar. Even if you kept fighting her forever you wouldn't win.

Once you get to Valor level 3 and become Valor Overpowered, you get access to the Instant Kill required to beat her.

The assumption made is that you need to land it raw (by itself with no attacks before), but this isn't the case.

Much like how in this mission when you land a Super successfully it launches a Bloody Valor afterwards, this can also apply for your Instant Kill. Once you have your Super meter full (all 4 yellow bars are full), if you land a Super against Satsuki, Ryuko will automatically use the last 2 bars for the Instant Kill.

This saves alot of time waiting for her to drop her guard (which the instakill can't break) or having the Instant Kill clash with another move she throws out. Instead you can do a combo that confirms into a super, which will save more time.

All Supers automatically go into Bloody Valor/Instant Kill.

Here is a video I made explaining everything listed here: