She drank some strong liquor but it didn't faze her.

Literal

She [topic-は] strong liquor [object-を] drank [but-が], nothing was.

何ともない is a useful set phrase meaning 'no problem, no big deal, it's nothing' — applied here to dismiss any visible effect from the alcohol. The が between the two clauses is the 'but'-が, a contrastive conjunction that clips two independent clauses together; it's milder than けど or けれども and very common in narration. A few alcohol-related notes: 強い酒 typically refers to spirits or other high-proof drinks (think shochu, whiskey, vodka) rather than beer or wine, and Japanese culture has a long-standing fascination with 'お酒に強い人' — people who can hold their liquor — partly because a real genetic minority of East Asians lack the enzyme to metabolize alcohol efficiently and turn red after one sip.