you don't kill them, they're kinda like walking dye tubs with rare colors. assuming it'll be the same principle as the japanese event, each slime spawned in a rare color. after a couple hours or a day the slime would go *poof* and respawn in a different location on the shard with a new color. they weren't killable. sometimes they banish you and you end up like 50 feet away from them and have to run back, and they zoom around but stay within a given location, so they're easy to chase. i think sometimes they kill you but i can't remember if the slime killed me or the spawn around the slime...
you take cloth, bags, backpacks, boots, etc. with you, and you chase the slime and when you get close you double click it and then you get a target cursor (just like a dye tub) and you click the item you want to dye
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. it's good to recall to your house or bank a lot and drop off the stuff you've managed to dye, so when you DIE you don't lose it all (if you can't get to your body, etc.)
some of them spawn in safe locations like zento or heartwood. some spawn in fel and are usually surrounded by a crew waiting to gank all the hapless people trying to dye stuff. that was a pita, but you just had to login later and try again. some of them are in the middle of dangerous locations like ilsh and you have to dogde and weave and try to survive while you dye your cloth. the teamwork in japan was awesome - there were always people stationed nearby with bandies and food and constant resses. it was a great community event
oh - and usually people will post here on the boards with slime sightings - since the slimes stay put for a while, it's pretty easy to get to each one before they relocate. so keep your eyes here on the boards during the event. the slimes spawned in different locations on each shard, during the japanese event. usually two were "live" at any given time, in differnet locations. Piel was awesome during the japanese slime event - she always hunted down the slimes each day and posted their color and locations.