Aye. Switches.

Basically you have an event with a conditional branch, and a handful of switches.

Each monster corresponds to a switch. For example, Mr. Slime could be switch [0001], whilst Mr. Big Shot Bossy guy is switch [0057].

When you go up to the monster (I assume that they'll be shown), the event that shows them is a conditional branch that checks if said switch is on. If it is, it stops you from fighting the monster. If the switch ISN'T on, then it sends you straight into the monster battle.

Assuming you don't die, at the end of the battle, that monster's switch is turned ON.

If you give me about 30 minutes, the once I've cooked and eaten my pizza, and hoping that the threatened Thunderstorm doesn't come, or someone else doesn't use the computer, I could probably toss a demo together for you.

EDIT: Unless, of course, you want to try it out for yourself first to see if you can get it to work.

If so, then you'd have to put the event in the Monster Group part of the database, to be triggered when the Monster dies/HP is between 1% and 0%... ish.