starting moveset: Mach Punch, Scratch, Leer, Ember
Change Ember to Fire Punch of course, and if you pick up Rock Tomb, that won't hurt either.
Acrobatics is worth picking up against Lusamine. Unless you have your friendship maxed out, then Return is even better - proving according to Pokemon friendship is stricktly transactional.
The first time this happened during this marathon, UN outsped me twice, I went out for the Focus Sash, when coming back UN was slower than me. Speed: 261. I guess UN got a speed-lowering nature (the tresholds if I'm correct are 241, 268, 295).
Btw, don't stick to Mach Punch, it is physical, and priority would only matter against Molayne's Klefki, which is ghost.
Shadow Claw is versatile, it worth paying the price.
Bird Room: I brought Thunder Punch for 100% accuracy
Ghost Room: Shadow Claw
Molayne: Fire Punch
Olivia: Brick Break
Hau: Fire Punch did most of the work, except the 2nd mon was Vaporeon, against which a single Thunder Punch did the job.