Always paired with 跟/和 (with) to introduce the opponent: 跟…对着干. Strongly colloquial — suggests stubborn or deliberate opposition. Slightly negative in tone when describing personal relationships, but neutral for business competition.
grammar
Structurally V+着+V: 对 (face) + 着 (continuous marker) + 干 (do/act). Literally 'doing while facing each other' — the 着 carries the sense of sustained, ongoing opposition.