It'll be changed in a few months but for now you can get some drinks from the bar in downtown and drink it near the end of the battle and it'll restore your "hp" making it unlosable
I tried this before trying to push him away but I still got the game over. I even had a full meal before going into this. Thanks for the tip though.
You need to take the drinks someways during the boss fight. Your tech at full "hp" when you start, so using them after a wrong choice or two.
