question: how do I beat aggressive players?

By making better moves than them. I just played one myself, wanted to see if this kind of craziness was common and that's how I got here.

15. Bh4 should've been Ngf3 of course, protecting d4 (and to a lesser extent d2, but of bishop takes, king takes).
Then to make matters worse I accidentally okayed a premove on 16. Bd8.
Apparently the computer didn't like 23. Kf2 either, but wanted to see Ne4, to attack f6.
Probably would've enticed them to take d1 as well, although, if I hadn't moved the king the rook on h1 would've been stuck.
Computer doesn't like 24. Rhe1 either, still prefers Ne4, which does make a lot more sense now.
25. Bxf3 and 26. Bxe4 it would've liked to have seen the knight take them, but if 25. Nxf3 who takes the knight on 26?

Anyway, just goes to show that if you don't panic you can even make a few mistakes/blunders youself. Because due to the nature of their playstyle they will more than likely blunder a lot more than you.

Unless of course they go Scholar's Mate or something, but you just have to learn how to deal with that one.
It's very easy actually: if you're playing black Qf3 => Nf3 (some like Qf3, but they might trade, which is not so good, cause there's a chance they'll give you their queen for free), Qh5 => g6, Bc4 => Nc6.
If Bc4 is played first followed by Qh5, after g6 some are dumb enough to go Qxe5 to plant their queen right in front of your king and then they'll have given you their queen for free because Nxe5.
If you manage to capture their queen, 99% of the time they'll resign, and if they retreat you'll probably win with ease because that was their whole repertoire.

If they're attempting it as black it's mirrored of course.

And I'm pretty sure 7. Qxg4 Bb4+ was a failed attempt at SM, which makes no sense given that their queen can't come in because of the bishop on g3 and my king can move about freely. And in this case they might've traded if I'd blocked their bishop with the knight, so the safer and simpler choice at that point is generally blocking with the pawn which is protected by the b pawn and the knight.

Edit: I'd like to also point out 30. Bxa2. Never forget the (defensive) power of your bishops. Just took out another rook in the same way. They will get greedy, they will want to prevent you from promoting your pawns, they want to create openings to promote their own pawns. They will forget about the bishop (or not notice him because he's so far away).
And don't be afraid to trade queens (or sacrifice yours if you've already taken out theirs and get a few minor pieces in return), because very often she is more important to them as an attacking piece, than to you as a defending piece. And it will greatly simplify things for you, not having to worry about queen attacks or defending your own.

Beretta M93R