In Mad Men S02E01, Peggy Olson becomes assertive, speaking up during meetings, even berating Lois at one point. Her entire demeanor had changed. But in subsequent episodes, this attitude change went away as abruptly as it appeared.
Peggy never loses this, in Season 1 she is new to the working world and the nuances of Sterling Cooper, however in Season 2 she shows signs of her maturity in her role and environment. It ultimately comes to a head in Season 2 Episode 5 where she is taking care of Bobbie Barrett after Don and her got in a car crash, where Bobbie offers Peggy some advice
"'You can't be a man', she advises. 'Be a woman. It's powerful business when done correctly'" (S2E05).
After this, Peggy begins calling Don by his first name instead of Mr. Draper, signaling a shift in her mentality. This continues throughout the show, where she often pushes back against Don and the other executives (e.g. getting Freddy's old office, telling execs to make their own drinks, confronting Don about GloCoat, leaving Sterling Cooper for CGC, and of course her famous Season 7 shot of her walking down McCann's hallway with a cigarette and Cooper's painting in hand)
The Chicago Tribune wrote up an excellent season by season breakdown of Peggy's arc: Peggy's Arc