Unless the enemy doesn't have any attacks, or your event is getting stuck somewhere, the enemy should at least start attacking once the dialogue is completed. In any case, you do have a couple options to force the enemy to take certain actions. You can use the "Force Action" command to make the enemy use an attack or skill. If you really want to deal specific amounts of damage to certain characters, you can use the "Deal Damage" command on certain characters, although you'll want to combine it with battle animations to simulate the enemy attacking.
You'll also want to utilize the event pages. If you want to control a certain amount of turns in the battle, you'll want separate event pages for each turn. Set the span of each page for "Battle" so that they only trigger once each turn and don't cause the battle to hang up.
If you're still getting stuck just let me know and I can go into more detail.
