I don't recall any relished victories I've had with a single player game, because the outcome was always predictable (fail and try again, knowing to use a different method, and then repeat until success). All of my proudest acheivements were against other players. One particular moment that I can remember was on SOCOM: Confrontation just last year.
I was in a clan war with other members of my clan, and it was the final round for the war. I was the last one on my team still alive, and there were 5 Mercenaries on the other team that needed to be elimated or our team would lose (suppression). They were trash talking the entire game, camping, etc. So in the last three minutes or so, I was hiding in an upstairs bunker taunting them over the mic (proximity chat)

I lured four of them one by one up the stairs by their own game, and got the four kills. The last one was staying downstairs below me in his hiding spot, still talking trash through his headset(going for the draw).
If I didn't kill him, our team would lose, so with 10 or 15 seconds left in the round, I ran downstairs with nothing to lose; machine pistol equipped, ran into the room, and sprayed behind the crates. The first or second bullet caught him with a headshot with one or two seconds left in the game

I started screaming trash in the mic over his body after I killed him, and once the teams were back in the lobby, the other clan bounced out without saying a word. I think karma is one of the most satisfying victories you can have online.
EDIT: The trash talking was simply is the spirit of fun (on my end, at least). It had everyone on my team laughing in the end. SOCOM is the only way that I get to spend time with my cousin, and our old friends since everyone has seperated and gone their own ways. It's something we've all been doing since at least 2002. Just a way to get everyone together once in a while and have a good time.
What made the victory even more amusing is that none of us are what you would call 'hardcore' players. For my cousin and I, this was our first night back on SOCOM in several months. So it was rather funny; a team of noobs silencing an alleged "hardcore, high-ranked, game battles clan", in the spirit of a good night. But tbh, I think the most relished part of the entire ordeal was just enjoying the reunion and sharing the laughs with my family and friends.
Kravenwolf