Harry's duel with Tormund Giantsbane. He doesn't even need magic to defeat the wildling chief - and it's just the beginning of Harry's task to stop the Others.
The big battle between Harry's people and Alfyn Crowkiller's. Even though they are outnumbered, the former handily win the fight with a lot less losses in the fight - and then they almost double their population.
The large battle at First Forge. All the wildlings that opposed Harry die, the others join First Forge and suddenly their population has doubled yet again.
The whole thing was a Batman Gambit by Mance Rayder: he sent the more Axe-Crazy wildlings to die against the well-equipped and well-prepared Norfolk, then ask for parlay and officially becomes Harry's subordinate. It has the double result of helping the Free Folk as a whole - by destroying the more unstable elements and joining a nation which will give them free access to prosperity - and to help prepare the Second War for the Dawn - by giving Harry new soldiers to train and a safe haven for the Free Folk. This guy didn't become the leader he is by collecting bottle caps, people.
Harry's travel down to the Seven Kingdoms. He manages to go from First Forge to Casterly Rock in just one day, reaches Oldtown the next, raids the Citadel's library, makes a detour to Dragonstone to heal Shireen Baratheon (getting as much dragonglass as he can take with him as a reward) and returns home. All in less than a week!
Really, what Harry did is enough to make him a King worthy of legend: not because he was a great warlord, but because he knew the wildlings could be great and prosperous, and so he gave them weapons, he gave them tools, he gave them crafts and he made them a nation with cities and trade and culture. The legacy he will leave behind is this.
They lose eleven men (out of twenty-seven) in the fight, but not only does the combined Norfolk-Black Brother (plus three Children of the Forest!) group fight off a battalion of wights led by three Ice Spider-mounted Others, but they manage to capture one of them!
After someone tries to kill Harry and his family via the Strangler, Harry orders no one will leave the town until he finds the would-be murderer. Daenerys and Arya capture the Faceless Man behind the attempt!
Harry infiltrates the House of Black and White AKA Faceless Men's HQ and manages to threaten the leaders so they won't take any more contracts on him and his people.
Dark as night, but Harry killing Grandmaester Pycelle for hiring the Faceless Men in such a way that people will think it was natural.
Littlefinger rightfully guesses that Harry was responsible simply by noting small but crucial details about Pycelle’s death. Say what you will about him, but the man is no fool.
