Peening isn't too bad, but the confines of the helmet make it a bit rough. You want to work in a "spiral", by starting on an outer edge of the rivit and working your way around and in. The idea is to spread the rivit wider, so that it holds itself in the hole. I see a lot of people who use a washer as a backer when doing it, but you shouldn't "need" a washer unless it's a sliding rivit or attaching a strap - at least, that's my understanding of it.
Halberds makes a neat hammer (
http://halberds.us/img/tools/newrivet.jpg) that would probably make it easier, but probably isn't worth the investment unless you plan to use it more than once.
I think the most important part would be not striking the rivit directly overhead. That widens the shaft by spreading it, and will make the visor harder to move. It might fix it as a temporary, but I think the constant movement might "saw" through the rivit over time. Or maybe that's what you need to do to tighten it?
Hopefully Allan can respond, I haven't swung a hammer for a decade and most of it was just working on existing pieces that I wanted to add straps or hinges to. Rivits are about the only thing I did.