Battling Solaris the second time.
I will be honest and say I didn't expect to actually be fighting him. I remember how my heart was almost beating out of my chest. The end of the battle was him vs Florina (my Pokémon were all knocked out). He had his Garchomp (if I remember correctly) and she had Torterra, I believe. I was so afraid that I'd lose the fight, but then (somehow) Florina took that stupid goddamn dragon down!
I know it might sound like a very lame victory since I didn't finish him off myself, but it still is a moment I find memorable.
Another one I am truly proud of is (in my first run), when I FINALLY beat Ciel.
I was a total noob back then. Didn't understand type advantage nor stats nor natures. Remember, I had only played a few games at this time. My strategy was kill anything on the field. At most times, it worked.
Not with Ciel, however. Ciel was a punch in the face for me back then. I remember how I sat down with a pen and paper and wrote down which Pokémon in my party would go up against Ciel's Pokémon (this was after she'd defeated me like ... the 100th time, or so if felt like it). I had no money to buy healing items nor common candy (and I didn't think about selling my crap). Half of my team was overleveled (Delphox, Stoutland and Glaceon) and I was beyond frusturated.
If I remember my strategy correctly:
Delphox against Togekiss. He had iron tail up his sleeve.
Ampharos against Archeops. I think, I'm not sure, actually. Anyway, I'm guessing she used Thunder on the thing.
Stoutland against Noivern. Giga impact. No more needs to be said.
Floatzel against Talonflame. That is, until it (somehow) knocked it out and I sent Delphox out so the bird out kill itself with flare blitz.
Not sure who I sent out against Gliscor. I think I did use anyone expect Glaceon, since I was spearing her for the big bad one.
Delphox against M-Altaria. Halved its health with iron tail. M-Altaria knocked him out and I sent Glaceon out and had her use Blizzard.
I just remember my reaction after having finally beaten the one gym leader that seemed impossible. I screamed. Yes, I actually did scream. I feel sorry for my dad, having to listen to me.