Some skaters that I think became transformed in a season are:
Michele Kwan in 1996
Brian Boitano in 1988
Angela N the year she went to Elena T
Patrick Chan (got a quad, improved his hands last season)
"Marge, if you're going to get mad at me every time I do something stupid, then I guess I'm just going to have to stop doing stupid things!" - Homer Simpson in the Mr. Plow episode
Same for Todd Eldredge and Punsalan/Swallow between 96 and 97.
And Anissina/Peizerat between 1997 and 1998. Gwendal was like a new skater in starting with that R&J program.
Yuna Kim from 07-08 to 08-09. I think this was the key moment when she's become more of a complete skater with unforgettable charisma and has begun her reign at the level of her own. For skating skills, scale of her jumps, interpretation of music, and every aspect.
Sarah Hughes between 1999 Nationals and Worlds amazes me (and Dick and Peggy too, according to their commentary.)
The skater who immediately comes to mind for me is Shizuka Arakawa.
I remember seeing her for the first time on TV at the Nagano Olympics in 1998 where she finished 13th. Frankly, I didn't think she was anything special at all. If you would've told me this girl would go on to become Olympic champion 8 years later, I would've laughed right in your face.
One of the best improvement stories IMO.
most improves skater ever: Yukari Nakano
Johnny Weir from his withdrawal to his first National Championship win. Not Michelle was that transformed the year of her first WC title.