The second boss is following a pattern. He starts by riding his giant chocobo, but you (controlling the bat) can interrupt his attacks/damage the chocobo enough to knock him off, which stuns him for your girls to grab. Once he escapes from a grab (or enough time passes without him getting grabbed,) he jumps back off screen and finally re-enters the battle mounted back on his chocobo again.
It's important to note a few things; when he's vulnerable to attacks, it's the circular icons that are the weak spots (when he's throwing up his spear, hit it to deflect or when he's charging with the chocobo, hit it in the eye) and you only need to interrupt 2-3 attacks before he falls off. Also, when he re-enters on a new chocobo, he ALWAYS lands with a rather painful ground slam (marked with three [!] on the ground.) However, you can control where this happens because it's always centered on the bat, rather than the girls. So if you want your girls to be fighting off to the side, drag the boss over to the opposite end of the stage and knock him down, then hover the bat over there while he jumps back in.
