Like the title says, kill the above person's avatar in any way you see fit. You could have your avatar kill it, or any other unsuspecting way.

GO!

I'll just lop ye' head off with me lightsaber, arrgh.

Schwing.

I just impaled you with my energy sword then shot you up with me plasma rifle. Finally I stuck you with a plasma grenade and would have blown you up except for that my game lacks extreme content.

Vrex, I just killed your avatar. WITH THE POWER OF ROCK!

I ram my scythe through your chest repeatedly, then smash your guitar, so the source of all your power is gone.

i throw you in a cannon and introduce you to the space progam.no suit

I'd jam my thumbs in your happy, happy eyes and pull your brain out.

I cut off your white streaks. With the source of all your power gone, you are helpless as I slowly torture you to death.

I summon forth a refrigerator and drop it on Azraellod.

I sit on you. Job done.

_{Good luck killing my avatar!}

I pour petrol on you, then move the burning guy a little to the right, causing you to catch fire and burn to death.

I sneak up behind you and backstab you. But first I kill your medic.

(Yeah, I thought it was a Jojo's Bizarre Adventure reference...)
Anyway, sticking with the theme of the manga, I kill you in some unnecessarily gory and disturbing way.

I take note of your movements, and trip you up at the right moment with a badger.

I turn off your tesla coil, exposing your fatal weakness, which I proceed to destroy.

I use splash! but nothing happened! -.-'

I cast Reflect on myself so that when you try to incinerate me, it bounces back at you.

I feed you into a combine harvester.

I place you in...THE COMFY CHAIR! (dun dun dun!)

I would probably introduce you to a mildly displeased bear.
gerr

by the way i think my avatars are almost imortal just saying

Not necessarily. My flaming skull moves over to your avatar and sets him/her/it/Tyson Rios on fire.

i just take you to England its always raining over here.

oh and do you know who you just killed

1: meet avatar.
2: hit on avatar.
3: ???
4: avatar catches AIDS.
5: painful, slow death.

I annoy you to death with my Caramelldansen!