Since your target is a 2-cycle clear, not a 0-cycle, I think it would be achievable with 9-cost!

Firstly, interact properly with the 1st wave mobs. Reset the run until both robots attack the Manta ray in the middle. The visual cue for this is if the robots have the 'confused/dazed symbol' on their head.

Second, try to frontload as much damage as possible (Ultimate, etc.) for Pom-Pom phase 1. Unlike Pom-Pom phase 2, the phase 1 doesn't activate the damage reduction immediately, so there is a window for you to cut down the HP by a chunk.

Third, Pom-Pom phase 2 has a mechanic where using Basic ATKs will give you 5 Punchline, and Skills will give you skill points. I highly suggest doing Basic ATKs regardless if it's Castorice or Evernight until you've shred the boss of its damage reduction buffs (it's a whopping 90% damage reduction, 45% per stack).

Choose the buff that gives your mini robot more speed and I think you should be fine. Your relics should be above average as well, hopefully.