Green’s Dictionary of Slang

one-on-one adv.

[one-on-one n.]

in an intimate, person-to-person manner.

[US]N.Y. Times Mag. 26 June 38: [They] suspect [...] that, one-on-one after a contentious primary, she will lose.
[US]N. McCall Makes Me Wanna Holler (1995) 270: I still had trouble relating to him one-on-one.

In phrases

go one-on-one (v.)

(orig. US) to have a direct confrontation with another person.

[US](con. 1975–6) E. Little Steel Toes 49: If Mopa and Liplock go one on one you don’t gotta be Farmer Flaco.
[US]C. Fothergill-Brown ‘WWE Confidential Report’ 30 Jun. 🌐 You see you stand now before The Rock, looking at The Rock, gawking at The Rock, wanting to go one on one with The Great One. [Going ‘1 on 1’ with the Great One = Home Run.].