I am rather confused by your question. I have just re-read both of these scenes and can't find any reference anywhere to imaginary animals. Do you perhaps mean real animals and birds? If you look at Act III scene 1 for example, there are a number of references to birds that are humorously used to describe the gulling of Beatrice. Let us look at those examples.
Firstly, as Hero and Ursula await Beatrice, Hero describes Beatrice approaching like a "lapwing":
For look where Beatrice like a lapwing runs
Close by the ground to hear our conference.
Lapwings are known for running along the ground to draw preadators away from their nests, and so we can perhaps appreciate the awkwardness and funny way in which Beatrice is running across the ground to "eavesdrop" on the conversation of Hero and Ursula.
Secondly, Hero describes Beatrice (to her hearing) as a "haggard of the rock," which refers to a wild hawk, emphasising Beatrice's "coy and wild" spirits. Lastly, a reference is made to a way of catching small birds when Ursula says to Hero, "She is lim'd, I warrant, you, we have caught her, madam." Bird-lime was a sticky substance smeared on branches where the birds were likely to land to catch them. The image refers to the way that Beatrice, like a bird, has been "caught" in the trap of Hero and Ursula.
So, although there are no imaginary animals, you might find it useful to analyse the use of animal imagery in these two scenes.