[verb (volitional)] + が [verb (volitional)] + と [i-adj 〜い → 〜かろう] + が / と [na-adj] + だろう / であろう + が / と [noun] + だろう / であろう + が / と
ようが and ようと mean "no matter what" or "even if": whatever the first half turns out to be, the second half does not change. They follow the volitional form of a verb, and the first half usually holds a question word – なん何, だれ誰, どこ, どんなに, いくら. The two endings mean the same.
The volitional here does not mean "let's" or "I will"; it only sets up the condition. A plain form in its place is wrong.
An い-adjective takes the old volitional ending かろう. A noun or な-adjective takes だろう or, more formally, であろう.
ようが and ようと are forceful and written; the second half is usually a firm resolve or something that cannot change. In conversation, the ても form says the same.
Two opposite halves in a row – ふろう降ろうがふる降るまいが, "whether it rains or not" – are the paired form, A ようが B ようが.