Is it illegal for an individual to record a boss yelling and using profanity at him?
New York is a one-party consent state, meaning that it is legal to record a conversation as long as one party to that conversation consents.
Unless you're subject to a contract prohibiting recording, or unless your workplace has some special characteristics that might interfere with your rights, you'd generally be within your rights to record. The fact that you're talking about audio-only makes it seem like you should be fine. This sort of evidence is pretty routinely used in employment-discrimination cases.
Probably not illegal, per NY Penal Law Article 250.
Yelling and profanity have nothing to do with it. "Verbal assault" is not a legal term.