From how I understand it, you can't lose a stock period, and selecting rematch doesn't work to get the achievement.
I did it on Normal and my strategy was to use a lifesteal spirit like MM Skull Kid and attached with it some health regen supports like meloetta or manaphy. Should keep you pretty low damage for most of the whole battle, and as long as you understand the other bosses moves in the rush you should get out of that relatively unscathed when it comes to the final battle.
With that fight I played it's safe and kept distributing my damage evenly between the two, that way I could get the "dizzy" state department happen one after another so I could get a solid amount of free damage (helps especially when you get it where one of them won't do that attack on the other until just the end of the knockdown time, prolonging the damage you can do to them. At around half health is the dangerous part, stay away from Mr Eyeball (not naming specifically for spoilers) since when he brings out his gun attack you can easily rack up over a hundred damage within seconds and since this is when they pull out the most devastating attacks it's crucial to remain low percent. At around 25% health I targeted one of em to make it easier on me and there's the homestretch. Just be patient and only attack when it's safe and you should be good.