I'll start off by saying my weakness:
Lag. Have you ever wondered why I suck in tight levels? Well, you will know now. Because of extreme lag in South Africa I never could do close battles. Heck, by the time I see someone it's already too late, I'm wasted! All tight levels limit 'ranged attacks' so you have to get close to someone to kill them. There, now don't host tight levels ya hear

Here's my battle tips:

1) NEVER STOP RUNNING! YOU'RE A RABBIT!!

Seekers and Bouncies are the best weapons. Sometimes I'll use RFs, but I actually prefer pepper spray above RFs.
No, I'm not nuts, I did some tests. Pepper Spray shoots farther than RFs, and just as fast. The pepper spray power-up shoots something close to 35 tiles far. Imagine shooting almost as far as a Seeker but as fast as an RF. Only problem is that it doesn't spread out, but you can do that by 'hopping' (jumping up and down in small burts) while shooting. Ok enough of that tip, back to my strategies.

2) I never shoot where a person is, but always where they will be. It takes a while to get used to, but if you shoot where they are on your screen you would shoot where they were (unless they weren't running, and what did I say about that ) and that's pointless.

3) I prefer to stay far away from the actual battles and use 'artillery' to blast in there. Bouncies, RFs, Seekers and Pepper Spray can all do some great artillery work. If you're far away nobody can hurt you, or sometimes even know you're actually part of the battle *evil grin*

4) Bouncies are just plain awesome. The only weapon that is not really affected by your running speed and direction. Ok well it is a little, but only a little. When someone follows you you can just turn around quickly, shoot a couple, and turn back and run. This saves the whole: 'turn around and run back in the direction of the person that attackes to shoot THEN turn around and carry on running'. Heh, I've killed so many ppl like this

5) The 'arc of doom' (mentioned by defalcon) is the best seeker strategy. I use it a lot. In fact, when I have seekers, I almost only use it. So there

6) Killing is more important than dying. If you don't believe me, there must be somehting wrong with you. You win by getting kills not dying all the time
Now, if you HAVE to stay alive all the time you've got some ego problem. I would much rather run straight into a battle near death to kill myself instead of clinging to life with one heart and no weapons, sitting in a dark corner hoping to reach a carot un-noticed. This takes TIME! And to buld up from that is very hard.
Heck, if you're in the situation, get yourself killed. Preferrably by someone low on the roast list (don't wanna give the winner a free roast close to victory). Yeah, that sounds good. Look for a n00b, have a little battle (you might just be able to kill him) and die to start again. He'll feel good and brag about his madskillz (not to mention play Jazz 2 more to try something like that again), while you get what you want, a quick full energy carrot. Every player out there has a purpose *evil grin*. Of course your reputation might not be what it used to be, but that little voice inside of you knows what really happened. DIE WITH HONOUR!

7) I always prefer a tactical advantage more than my own life. It's stupid, and you most probarly will die, but chances are you will get a kill before you do. If you're about to die, and some L337 demi-god whose only purpose in life is to give you a quick death guy with a fastfire powered up bouncy comes from above, you will have a choice to make. You know there is a carrot underneath you not far away that you can run for, and you know there is some really mean weapons above you, it would be pretty obvious to choose to run like crazy to that carrot as fast as your shaking little legs can carry you. Well, I wouldn't, even if I only have one heart I'll take a chance and try get above the guy. You might think this is suicide, but the other side is as well. That guy almost definitley knows where the carrot is, and he will know you're going for it, so it's ok for him to kill you there. Or, even worse, the carrot was taken. Or, even worse, the carrot was JUST taken and there is some major battle going on there. There is always activity close to a carrot, it's probably the most active area (or close to a power-up. If you're above the guy (and you survived) you at least have tactical advantage, so you can attack him as a bit of a 'back off' warning. They might be persistent and follow you, but (if you manage to live long enough) will waste a lot of ammo and loose some life before he kills you, and he'll end up being in your situation. Just a bit of revenge

8) Just another interresting little fact. Jazz/Spaz moves at 20 tiles per second. That means that if you stand still, someone that is running will reach you (from the edge of the screen until he touches your bunny) in 0.5 seconds. If you're both running at each other, it will take 0.25 seconds. Heh, that's some major reaction time. Next time someone runs flat out at you and you dodge them, remember that you did it in less than a quarter of a second, you can start feeling proud now
Unfortunately, this also means that you need a ping of at least 250 to be able to play jazz properly.

9) Hmmm, last thing, the tips on J2O are wrong (the one about the non powered up bouncy going farther) in a way. It only goes farther because if the powered up bouncy bounces back again when it's almost done. All you need to do to prevent that is to jump in the air before you shoot, so it won't bounce backwards

That's more than enough, I love free periods during school