update, I wOn a battle and it let me turn it in. which is not the same thing as the quest description which simply says to "try a battle"

maybe the description should be changed to say 'win a battle'

You can also just start the battle and then hand in the quest, as simply starting the battle counts. Meanwhile as you already discovered losing a battle doesn't count so if you are having trouble with battles you can just start them and then click out.

Hmmm I do wonder if 'Start a Battle' might be a better phrasing for these quests, since unfortunately losing a battle doesn't count (it is a known issue). But start might better imply that you do not need to finish a battle in order for it to count for the quest, since I know this comes up a lot.