I found a strategy on Reddit I was able to copy.
You have Elincia and Iote's Shield (although I guess any brave weapon with enough speed to quad will do), two ranged dancers and one melee dancer and get them in the following position:
Claude will always attack the melee dancer since they can't counter and all you do is attack with Elincia four times every turn and ignore reinforcements. Elincia has breath of life to heal the dancers and noontime to make sure she always has enough HP for guard to be active. The melee dancer has guard too so Claude doesn't build special off her, and all the dancers have Spur Atk and the Spur Atk/Drive Atk/Attack Tactics seals to maximise Elincia's attack (maybe I only needed them because mine is -Atk though).
It still took me several attempts because depending on what reinforcements you get they might change Claude's AI and mess everything up. On one attempt a red unit spawned near Young Azura and got her to low enough health that Claude moved and attacked her since he could kill her, and on another a bow cavalier spawned and attacked Elincia from the defense tile so she was no longer in guard range so Claude was able to get special charge and messed up my positioning.
Also, if Claude has already taken some damage before you start and you can reduce him to 1 HP before you reach the 150k target, noontime will no longer heal Elincia so she'll quickly go out of guard range.