Let the wolf run the hen house – let the wrong person be in charge.  Allowing someone to be in charge who has an biased interest or conflict of interest in the situation.

His bark is worse than his bite – Someone comes across as being very mean and nasty, but doesn’t necessarily act on their threats
have bats in the (or one’s) belfry – Informal. to be mad or eccentric; have strange ideas
busy as a beaver – Busy.  Beavers are  notoriously busy animals because they cut down trees to build their homes on river banks.
the bee’s knees – the best, superior, the cat’s meow
a little bird told me – I won’t tell you who told me
bull-headed – to be stubborn
I chose these ones from this website.  You can look there to find lots more animal idioms.