Need some help with an Eidolon battle.

Eidolons are tricky. For most of them you'll be changing Paradigms pretty much every moment (don't ever delay!). If you have any Fortisol (or whatever it is that had Haste) throw that on. It really helps. Aegisol will too, but those are very rare and you'll probably want to save those for much much later (you can't purchase shrouds until the end of the game, except for Ethersol, which you can never buy ever ever). This is how I typically go about it:

Useful Paradigms:
MED/MED
COM/MED
RAV/MED
COM/SYN
COM/RAV
RAV/RAV

First I throw on some Fortisol so they're nice and speedy. I start out with Hope as a SYN so he can cast Protect. I can't remember if Shell is necessary. If he has magic attacks then definitely get that ready too. Then you just wanna build up your chain. RAV/RAV is best for this, if the chain starts depleting too quickly just have a Commando whack it a couple of times to stabilize it. Just build up that chain and be ready to switch to MED/MED or something with a Medic at a moments notice. If you need to heal then you really really really need to heal. The most important thing is to be very quick with your healing, and don't let Medics linger for too long. You gotta build that chain to boost your Gestalt!

In summary: Protect, maybe Shell, CHAIN CHAIN CHAIN, heal quickly and move on to chaining again.

EDIT:

About chains! This isn't always obvious to everyone, so I thought I'd give you a tip in case you didn't catch on. It's vital information! Ravagers build chains up very quickly. Commandos build them very slowly. However, if you use nothing but Ravagers, it'll go down faster than it goes up. The trick is to have a Commando hit the enemy first. Then the chain will lower very slowly. After it's been stabilized by a Commando you can just switch to a full party of Ravagers and watch it go zooooom~