I was going between random profiles for my likes list, and on Flute's page, when I scrolled down, there is a Trophy Collection???

What is that, and why have I never seen it?

I've definitely seen this on older players before, my guess is that it has to do with some contests and etc that took place years ago.

from what i can remember it was link to some kind of achievement from 2013 to early 2014 that was put on hold as it was laging the site or somthing like that, i joined after they were discontinued so i can't say too mutch about it unfortunately.

Once upon a time we had leaderboards for things like pet with the highest agility stat or player who has bred the most pets this week or player who was first to complete the brand new dungeon. For various reasons like lag and categories becoming irrelevant, this feature was removed. But you can still see it on the profiles of older players.

To add to Sakina's explanation, there can also be trophies on pet profiles for the ones specific to them. Here's one as an example.