See my Patch 4.2 Rare Pet Briefing Post for an updated guide on how to tame Kirix, as well as the other 9 Patch 4.2 Taming Challenge pets.
Kirix is a rare spider that will be added in Patch 4.2. He is among the eight new taming challenges that Blizzard is providing in the Firelands patch. Each one of the eight pets is supposedly going to require the hunter to approach the tame with some sort of strategy.
The difficulty with taming Kirix appears to be his Toxic Presence buff which causes nature damage to all nearby players. The player in the video mentioned only being able to survive within it for about three seconds, so it hits for a considerable amount of damage.