I don't think the petpet battle high scores work like that. It goes by level of your petpet and wins for the day I believe.
i.e. I win 30 battles and only have a score of 10 for a level 1 (well level 3 after winning 30 battles) petpet.
The highest possible score is 38 for some reason and there is a total of 33 possible wins a day (bug that doesn't count the actual winning battle if you win 10 in a row) even though it says 30. It seems any pet over level 20 or so can score a 38 by winning all 33 battles for the day.
This game is very buggy, open to cheating, and predictable.
Don't bother trying to get a high score unless you know how to cheat it, because as soon as the scores reset at the month's start people already have a score of 38 the same day; taking all the trophies.
I offered to point out all the problems to the Neopets.com team, but they decided they didn't care when I emailed them about it.
On the upside, once your petpet hits about level 35 it can take a good 45 minutes to win a single battle, so these cheaters have to reset their petpets a lot.
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Neopets should invest some of this promotional money into making the site secure and less prone to cheaters....And fire the idiot who thought Kauvara's Code was a good idea.
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EDIT: For the average person a good strategy is start with Head Shot and keep doing that until you notice you aren't doing any damage and taking some. Switch to Body Blow and do the same. Use your shield when the opponent is 40% or below OR you are taking a lot of damage and hit 50% before the opponent goes below 80%. Doing this should take you up at least one level a day unless you get unlucky