Dos-Ryga

• 
  
• Start with [petability=256]. Use Scourged Whelpling of any quality, even freshly caught, don't need to be max lvl. Could also use any other pet with this ability as long as you have it with 700+ HP (more if it's Mini Diablo).
• 
  
• Switch to one of those foxes. Need only lvl 21 blue (rare quality) to survive Whirpool (again, don't need to be max lvl) so better to use Kun-Lai foxes since you don't need to level them, but it's ok to use any other pet that uses both abilities if you have it on high enough lvl. Use Dazzling Dance and Howl (in that order).
• 
  
• Switch to one of the pets that use [petability=517] (any but the bats or Bone Serpent will do). Use [petability=517] and if it didn't crit than finish off with Alpha Strike, Quills or Peck.
  
  This can only fail if you'll get unlucky Whirpool timing which happens rarely or (unlikely) misses.

I used the Fire-Proof Roach as my first pet. Used the ability Apocalypse. The ability killed him when the meteor hit, after 15 rounds. I guess any roach or beetle with the ability would do.
Edit: The roach does not have to be alive or the pet in play when the meteor hits btw. (thanks huspomike)

5.3 Easy Mode strategy

So, the 5.3 change basically made his heal twice as powerful as before, so the key is to be able to burst him down in that 5 round window. Chrominius is the real key to this strategy, and then follow him up with a Crow/Gilnean Raven.

1. 
   
2. Open With Chrominius
3. 
   
4. Dos-Ryga uses Whirlpool
5. 
   
6. Chrominius uses Howl
7. 
   
8. Dos-Ryga uses Healing Wave for 0 health
9. 
   
10. Chrominius uses Bite (400+ damage)
11. 
    
12. Dos-Ryga uses Frost Breath
13. 
    
14. Chrominius uses Surge of Power (1000+ damage)
15. 
    
16. Chrominius eats another Frost Breath and dies to Whirlpool
17. 
    
18. Gilnean Raven Uses Call Darkness (200+ damage)
19. 
    
20. Dos-Ryga uses Frost Breath
21. 
    
22. Gilnean Raven uses Nocturnal Strike (300+ damage)
23. 
    
24. Dos-Ryga dies
25. 
    

The fight will follow this script every time as far as I can tell. He always uses Whirlpool and Healing Wave on Cooldown, in that order, and fills in with Frost Breath, so you get 5 rounds to kill him. Chrominius' 1400+ burst in 2 rounds trivializes this encounter.

Enjoy!