According to Alveiah on the (WoW forum](http://us.battle.net/wow/en/forum/topic/9423382936) it is doable with the following tactic:
did it as frost. I started away from Nibbleh in the corner on the same wall and turretted until he caught up to me, then blinked to the next corner, repeat, blazing speed to the next corner, repeat, after that you have to move a lot more and get creative / be careful with your kite path.
And Exhortium on WoWhead
I completed Nibbleh as a Frost Mage ilvl 544 with Legendary Meta and Cloak.
The Talents I used include : Ice Floes (For casting while moving when procs are unavailable), Ice Barrier (Cause to heck with his damage output), Cold Snap (His damage is high and a 30% heal is almost a must!), Living Bomb (For single-target pewpew) and Invocation (RoP is useless and IW is iffy)
I used Master Healing Potion to heal the damage he outputs, 300 stat food and flask. I also of course has my class-specific buffs such as Arcane Brilliance, Frost Armor, Time Warp and my Elemental.
To defeat Nibbleh I used the "Downstream, Upstream" method which has been shown by others on this page. I began the fight at the south-east corner of the room and used Invocation. As Nibbleh spawned I popped Time Warp, applied Living Bomb, threw out Frozen Orb and stayed as far back as I could while throwing out Frostbolts (If you manage to get 2 Fingers of Frost and a Brain Freeze proc, don't be afraid to pop Icy Veins and Alter Time to get more burst damage out).
After he reaches your destination begin to move as close to the green slime as possible WITHOUT allowing him to touch it and proceed to back-peddle while throwing out procs, keeping up Living Bomb and using Ice Floes where no procs are available. Also, do not forget to avoid the pools he spawns. If Ice Floes has no charges, you have no procs and you do not have enough room to hard-cast, spamming ice lance is still free damage!
Again, as you reach the north section of the area and he is about to reach you, begin to go south alongside his poison trail avoiding any pools he may have placed. If all goes well and the odds are in your favor, you should be able to defeat him. There are of course many ways which you can be cheated out of your kill, either by him stopping randomly due to a bug or pools being horribly placed.
Things To Remember
Do NOT use Mirror Images and keep an eye on your pet as these have shown to pull aggro in my past attempts. Mirror Images is only a last ditch attempt cd and should otherwise not be used.
Always keep an eye on where he places his pools as this can and while get you killed!
Be careful when using alter time or when you are turning to kite Nibbleh up the next line as it may delay him long enough to get a stack and this can completely ruin an attempt!
Remember to use your Master Healing Potion and Cold Snap if you are low on health and keep Ice Barrier up as much as possible!