Well, my first attempt is *drum roll* ... Fairy Ferret! That's after a 17 hour Koala to boot.
But there are so many good possibilities here, the chances of getting at least one of these animals should be pretty good. Might as well keep a record:
Water-earth-nature-fire (14 possible good results / 23 possible fails)
1) Fairy Ferret
2) Rainguin
3) Fairy Ferret
4) Fairy Ferret
5) Fairy Ferret
6) Seamur (new animal!)
7) Fairy Ferret
8) Rainguin
9) Fairy Ferret
10) Armordillo
11) Jackalope
12) Turtisle
13) Bamboon
No luck getting any limited animals, but at least I got Seamur.