In Year 2, Harry gives Riddle an awesome"Reason You Suck" Speech ending with Harry declaring himself the Heir of Slytherin.
Directly related to the above, because Harry's rescue of Ginny was a result of Percy's direct request and offer to exchange his life for hers (believing Harry to have been the Heir all along), Harry, Draco, and Theo manage to pressure Percy into binding himself as Harry's personal vassal. This marks Harry's first step on the path to becoming Lord Potter.
Harry's takedown of Theo's prejudiced attitude against muggleborns and their descendants, in what becomes a simultaneous Patrick Stewart Speech and a "The Reason You Suck" Speech. So powerful that the entire Slytherin class (and everyone else who happened to be at breakfast at the time) took note, and even Draco acknowledges its merit.
Harry gets a big one in Year 4. During the Third Task of the Triwizard Tournament, unlike in canon, all four champions make it to the center of the maze. Harry faces off against Fleur Delacour and manages to best her despite being at least three years her junior in terms of magical study.
Though only after Fleur breaks her arm and has to fight left-handed.
The duel between Cedric and Viktor Krum, though we only see brief bits of it, is no less epic. The two are trading spells at a furious pace, so much so that Harry is left in awe.
Harry then manages to distract Cedric and grab the Cup before Cedric can.
In year 5, Harry succeeds in reconciling the differences between the Malfoy and Black clans.