A lot of people have problems with this challenge and complain about it in Housing /zone chat on a daily basis.  For one of my plots, I needed the Altered Web and had to do this a lot.  So, here's the best way to do the Challenge: Guide to Defeating "Eggbeater:"

• 1.) Equip a Support ability that will heal you and that you can chain cast (ie. has no cooldown).
• 2.) Anachronondax will lay two different types of eggs - Tainted Eggs and Spider Eggs.
• 3.) Do NOT destroy the Tainted Eggs!  They do not count towards Challenge Completion and spawn an add or squash entrails. 3a.) You can kite her through the entire Spiderland plot without fear of resetting her.  You need not stay in the encircled area that she begins in.  3b.) Her AOE/telegraph can break the Tainted Eggs, so make sure you do not face her towards Tainted Eggs! 
• 4.) When Anachronondax lays a Tainted egg, kite her away from that egg to the other end of her plot.  The egg will despawn in a few moments.
• 5.) When she lays a Spider Egg, pull her away from it a bit and run through her towards it to attack the egg.  This guarantees you won't hit her too much and kill her before all the eggs.
• 6.) Heal yourself between Spider Eggs and be patient.  She often lays a chain of Tainted Eggs and you will normally have between 0:30 and 1:30 left on your timer when you kill all the eggs.  

The biggest secret to this is Challenge is not killing the Tainted Eggs and not killing Anachrondonax before you complete the challenge. With the above strategy, I was reliably and painlessly able to defeat the Eggbeater challenge consistently while I needed to farm it. Good luck!

To do the Eggbeater challenge on this plug, you need to wait for Anachronondax to lay eggs and then destroy them.

Large Spiderland FABkit Size: 1x2 Requires: 41+ Source: Challenge Special: Eggbeater