Drowning the Alliance

If you're looking for the damn quest on your alt and can't find it, it's because you have war mode off.

You're welcome.

As with most quests, this cannot be done in a raid. It's definitely a good idea to form a group, but limit it to 5 people. You can always have other groups along with you helping out, just don't convert to a raid.

YOU CAN DO THIS without friends or a second sub, provided your PC will load up fast enough for you to get the kills before your character de-spawns.
As mentioned by others, BOTH characters must be on the SAME or CONNECTED servers or they won't be able to see each other.
I did this method w/ 2 80's (I assume within 5 levels of each other will work but didn't test).
Set both characters in WM ON and park them near the graveyard in Nazjatar /way 41.5 57.5
You then need to alt F4 out of the character that will be killed and immediately re-launch the game.
You will have approximately 60 seconds from the moment you press alt F4 to complete each kill.
Log into your other character and kill the target character as fast as you can. (I managed consistently about 45 sec each time from alt F4 to kill and I don't have a super fast setup).

Think of it like this: It's actually a lot faster than the "natural" way. No PvP skill/gear required, and no hoping people will show up in what is a mostly dead zone these days. Sure, it's a lot of logging back and forth & waiting to resurrect but take comfort in the fact you did it all by yourself.

A couple tips to save you a few valuable seconds (and repair bills):
Remove all armor/weapons from target character. Disable addons for faster load time.
Hope this helps someone.

Cheers!