The phrase "on sly" generally means doing something secretly or stealthily. When it comes to finding antonyms for this phrase, we might look for terms that connote openness, honesty or transparency. Words like openly, overtly, directly, candidly, straightforwardly, and honestly can all stand as antonyms for "on sly." These words convey the idea of doing things in the open, without any hidden agendas, and with complete honesty. They can be a useful way to distinguish someone who behaves in a straightforward, transparent manner from someone who operates in secret, without revealing their intentions or motives.