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 shoot up with my favorite plasmid, and what more can i say? I take aim for Azraellod and Incinerate!

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 pull a lever and a piano drops on SirBryghtside.

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

You are epileptic.

Try your best little man. For I vill crush you.

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

I Za Warudo you and give out a glorious battle cry.

(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 blow your arms and legs off with Alucard's Jackal and leave you to let you bleed out.

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 play Mozart towards you, making your foul rock-embracing form explode.

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

I fry you up and serve you with a side of lemon.

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 toss you too into said 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

I stab you with the Master Sword, which is on fire, throw you in the air, then shoot you with my bow thirty times before you hit the ground.

I throw my giant ninja star at you, cutting your head off

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

I annihlate it with MAH CANNONS.

Who will dare challenge me? A war machine taller then Taipei 101.