This looks an awful lot like a basic English SVO sentence. No "bod", no conjugation on the verb, no "yn". What's going on here?
This is an error, the sentence should be 'Megan sy biau'r gath!' - 'Megan (who) owns the cat'
Although a better translation of its true meaning would be 'The cat is Megan's'
Oddly, piau/biau is a actually a conjugated verb, although a very irregular one. sy has no grammatical function here, but it is usually included in the colloquial expression. sy is not used in this construction in more formal registers of the language.
The unusual word order is because the construction is emphatic - the 'owner' is being emphasised, so it moves to the start of the sentence.