Even if you're low level and can't actually help much with damage, it's still a good idea to check the reinforcement requests periodically. You always get one free attack against each, which is enough to get a participation award and a defeat count, and those can seriously add up.

For conquest battles, TP recovers over time, but it's pretty slow. But if your TP isn't at max you'll get a drop that restores 40 TP fairly often from quests. If you're still getting unlimited AP you can actually solo at least some conquest battles by using your TP, then spamming quests until you get restores, rinse and repeat. AP doesn't recover fast enough to do that once the unlimited is gone, but it still seems like a good idea to go into a conquest with full AP so you can get some extra licks in.

There's also something called a Revival battle, which works about the same, except instead of having a fixed timeslot for a guild, you can start one once a day (or join one started by a guild member) as long as it's not too close to the scheduled conquest time. There's probably some difference in the rewards, but boss cups seem to be rewarded the same way.

I hope whatever the event is doesn't require doing a lot of conquest battles, because there's only one window where I'm not typically asleep or at work.