Its your basic Quest druid, with a little extra flair with your fat old beasts.

Basic game plan:

Aggro - With this match up you have to weather the storm - tank up on all your armour until you've got a chance to play your big bois. The 4 drops all have 1 health, so trying to complete your quest that way is probably gonna get you killed. Having the big bois will (hopefully) help you stall up until the point where you complete the quest, and play Ultimate Infestation, and can play 5 phat bois on turn 10. Most aggro decks you face won't have too much mass removal, so don't be scared to fill that board up.

Anything else - Mix of armour and removal. Your Cursed Disciples will be a bit more sticky whilst providing good trade opportunities for pretty much all enemy minions, and your Steel Ragers are a good pull from Oaken Summons for some more speedy removal. After you complete the quest, don't throw out all your minions at once - the last thing you want to do is have them mass removed or shuffled back into your deck (to full cost) by a Psychic Scream.

In terms of the big bois you have (i.e. every minion over 7 mana), having them as beasts aren't absolutely crucial - I only have it going on because I packed Tyrantus and this seems to be the only viable way to use him. Furious Ettin is a notable inclusion if you're missing some of the more expensive, and be sure to take out the Stampeding Roars and Oondasta if your beast count is particularly low. Good replacements for these are either some Ticket Scalpers (another 5 attack that can be pulled out by Oaken Summons, that also has card draw), or an additional Ultimate Infestation for some late game shenanigans.