"Wildly" is an Adverb.
Adverbs modify verbs, adjectives, clause, phrases, or another adverbs, meaning that they can describe how, where, when, to what frequency, or to what extent an action takes place.
There are many types of adverbs, "wildly" is an example of an adverb of manner as it tell us the way something happens. In the sentence, "wildly" describes the way the pink pig clapped.
Other examples of adverbs of manner are softly, terribly, sadly, happily, carefully and carelessly.
