First, it's not possible that you don't have Ifrit. Second, you have Bahamut? You got through those three uberpowerful Ruby Dragons and beat Bahamut and you can't beat Adel? (I'm not making fun of you at all, I'm just saying beat Adel is easier than getting to and beat Bahamut)

Anyway, Adel can have 10,000 HP, she can have 51,000 HP. Those are her limits, and it all depends on the level she is at when you fight her, which depends on the level you are at. Here's what you want to do. First, draw and cast Regen from Rinoa onto Rinoa. This will save her from Adel drawing HP from her. During the fight with Seifer, he may have had Aura which you could have drawn. This spell allows you to do Limit Breaks when your HP is high. If have that spell, wonderful, if not, it's not the end of the world. Now, magic is going to be a bit useless in this fight, because Adel's Spirit is much higher than her Vitality, so make the Strength stat your priority when junctioning. You will want your fighters in this fight, namely the boys. The girls aren't bad, but the boys have much better limit breaks for this battle. So, if you have Aura, use it. Irvine and Zell's limit breaks are pretty safe. Squall's is iffy depending on the weapon you have. Most of Irvine's limits hit just Adel, so use them. Squall's limit will just hit Adel, but his finishing blow might hit Rinoa as well as Adel, if he even uses something other than Rough Divide. Zell's limit is what you want to use a lot. You can perform a series of repetitive blows with his limit that are really easy to execute and always follow each other. All you have to do is alternate between Punch Rush (O X) and Booya
(<- ->), whichever comes up first, start with that, then alternate. You can repeat these two an insanely large amount, doing massive damage. So my suggestion is this: Have Squall be the healer. Have him cast Regen on Rinoa, heal when necessary, and attack otherwise. Have Zell and Irvine use their limits, either with Aura or with low HP. If Irvine runs out of ammo, make him the healer and use Squall's limit. Be careful, if Squall's final blow hits Rinoa, heal her immediately.