I got my 300 losses in last night in case I didn't manage to do any more today, and while it would've gone fast with a Play Again button, I found it wasn't too bad. I figure I'll share this in case "play again" gets taken away for whatever reason - basically, when I finished a fight, I didn't hit "exit" (I tested both ways, and it wasn't necessary to press it for the win to register). Instead, I pressed backspace on my keyboard, which took me back to the battle setup page (equivalent to clicking on the Back button once), and from there it's only four clicks to start a new fight, I think ("continue", "challenger", difficulty selection and "battle").
Bif - originally, I wanted to get my wins and losses wholly in with my battle pet, and leave all the rest of my pets without a BD record, hence going for the "slow death" option rather than picking one of my punier pets. When I realised how tedious that would be with this set of battles, though, I abandoned all my principles and fought with my low-hp plushie ixi
(I figured it makes sense that a soft toy can't win a fight.)