On the road to Cameran, Ash is attacked by a Lucario and perfectly holds his own! Sure, he gets a broken arm, but he shows off the ability to use Counter to give her a broken rib!.
Really shows how much Ash and Pikachu changed since then. note In Pidgeot's case, against a flock led by a certain Fearow
Butterfree and Pidgeot show off their BW levels, gained after 4 years of protecting their flocks.
Pikachu: Ash, you did remember to clean its cache once in a while, right? note 'It' is Dexter, his Pokédex Saphroneth always seems to capture what the Pokémon and Trainer mean to each other perfectly.
Whenever a main character successfully Mega Evolves a Pokémon for the first time, which involves the trainer focusing on their bond with said Pokémon.
Or how Misty, the youngest member of the Kanto-Johto Elite 4 in centuries, can casually send three opponents twinkling in the sky. Now you understand why a Gym Leader is so respected, and him going all-out is something everyone fears. To get in the Elite 4, you must prove you can fight Legendaries evenly when at a disadvantage when it comes to type. To be a gym leader, you must take your own team and/or rent-a-Pokémon and give a good showing against a member of the Elite 4.
Qualifying as Gym Leader or for the Elite 4.
A slight one for the author by managing to get a pretty accurate guess on how Keldeo would be depicted well before his featured movie was released.
Just seeing Ash going mano-a-mano against Pokemon on his own is one.
Gary is initially angry that Ash's Squirtle turned his Squirtle into post-time-skip Simon (not literally).
Ash's Squirtle is a walking, talking, Tengen Toppa Gurren Lagann reference.