I'm more than twice his age, and if someone bet me on whether or not I could "get an achievement" I'd totally consider this fine.
Until more details came out, I actually thought the OP was paying to have someone get it for him so he could look like he did it, and was all ready to throw insults until I realized I was wrong. Still, the kid DID get the achievement; now you gotta nitpick HOW he got the achievement. Good luck. From now on, you're that teacher who doesn't follow through with his promises. Have fun with that.
When I did an afterschool program for fourth graders, I made a bet that I would buy everyone pizza from a local restaurant if any one of them beat me at chess. I made SURE that I was crystal clear about the rules and no cheating. One kid tried to cheat, and would have pulled it off, but his classmate told him it wouldn't work and made him play fair. I also bought those damn whippersnappers their pizza when I finally lost. The moral of the story is, you need to be clear on the rules, you need to do what you promise, and you need to offer an appropriate prize if you're going to make a bet with children.