I was playing AC Shadows recently and after dancing around a big armored guy to whom I wasn't doing too much damage for a while, I managed to kick him off a castle wall. As he was flying down, I thought "huehue, this is Sparta." A moment later, I get a pop-up saying "This is Japan, actually." Magical and hilarious moment.
I view achievements as something that provides value to games I really like while being easy to ignore in games I don't. Occasionally, they can also yield super memorable pats on the back, like AC Shadows did for me.
I'd prefer if Nintendo embraced them, especially since a decent chunk of their studios take the time to implement per-game achievements, but I'm not holding my breath at this point.