When the two words "boggy" and "twat" are used together, it becomes a phrase that is used as an alternative way of calling someone any combination of basic swear words like f*cking b*tch, f*cking c*unt, dumb*ss b*tch, etc. This phrase is considered as a more humorous way of insulting someone and is usually used among friends as a joke
Mike: "Hahaha...bro you're such a little b*tch sometimes"
Alan: "Hahaha...shut up you boggy twat"
Someone who is difficult to distinguish if they are a boy or a girl, so they are just a BOG, or Boggy.
Shitass Bankteller: Dude, is your cousin a boy or a girl?
One soon to be nicknamed Boggy: She's a girl, dude.
Shitass Bankteller: So she's a Boy Girl...a BOG...we should call you BOG...Boggy.
Boggy: Dam.