Doesn't appear to matter, as long as you kill at least one. I was instance-hopping this morning, and during the event, got in on at least half a dozen battles. they just call them out in zone chat, and go from one to the next. If I didn't kill any, i didn't get a reward, but as long as you get one and get the 'battle' music, you're good.
Would be nice if they fixed the pvp race so you can't cheat. Ran it this morning, and took an early lead, no one ever passed me. got to the end, only the 2nd place banner remaining. Took about a minute afterwards to find that there's a clear path to just go off the track and right to the end, must have been what was done. Kinda lame.
Also, what do you do with the Epohh tags? running the BOFF mission, but otherwise? do i need more stuff to kick off the breeding thing? No idea haven't done it on New Romulus either.