This is not a refined deck list yet, just something I threw together to complete the "play 12 beasts" daily quest and performed better than I expected. I did draw Vanndar every time though.

Compared to other Guardian Druid decks, this doesn't doesn't go up all the way to Survival or Clowns, instead focusing on putting a lot of stats on the board after turn 5. In particular, this deck runs 7-8 mana beasts that end up below the 5 mana boundary of Guardian Animals after being discounted by Vanndar Stormpike.

Mulligan

Toss everything you don't really need to find Vanndar.

If you think you'll be under early pressure, Partner Assignment, Nature Studies, Guidance and Teacher's Pet can be a keep. If you think you'll have enough time, Overgrowth is a keep.

Keeping Guardian Animals can be viable, but only if you have Overgrowth or Lightning Bloom as well.

Replacements

Guardian Animals and Vanndar Stormpike are essential. Druid of the Plains is a key card, but you could try play with one copy or none. The other epic and legendary cards should be easy to replace.

I saw Strongman in other Guardian Druid lists and while this deck doesn't run a lot of cards over 7 mana, the fact that Guardian Animals is 8 mana means you will be likely to corrupt it. However, after playing Guardian Animals you're probably already in a good position, so Strongman might help you at the times when you least need help.

Living Seed could be useful to tutor beasts, since it is essentially free to cast on turn 5+. In one of my games I discovered this spell via Nature Studies and drawing a 0-mana Moonfang after Vanndar proved to be very useful.

Deviate Dreadfang is something I threw in there to test. There may not be enough Nature spells in the deck to make it worth it.

One copy of Primordial Protector might be worth it to tutor Guardian Animals.

If you want to add card draw, Moonlit Guidance is probably better than Guess the Weight, since the deck cares more about finding specific cards like Vanndar and Guardian Animals than about drawing lots of cards.