By exhilarating, I mean things like boss battles that you were not NEARLY prepared for that you somehow beat. If you want, you can also add some advice to how you did what you did/how it happened.
Personally, I was on a multiplayer world with an AFK friend when Skeleton Prime spawned. We had been preparing for him but we weren't nearly ready. Somehow we still managed to beat him just before morning, which felt fantastic.
Heh. Oh this is an easy one. On my most recent playthrough (Yes, the one which i had the crazy seed thing), i defeated the Eye Of Cthulhu with wood armor. Although, to be fair, i did have the Undertaker... and maybe an archer potion & night potion (Not that that mattered, i didn't even have the defense bonus as i opted for a mining helmet instead of wood helmet. Now im in full crimson armor.)