I will totally admit to spending way too much time trying to get trophies in Fallout: New Vegas, but I’ll just say that many people have suggested gamifying iNaturalist, and it’s not something the iNat team is particularly interested in.
Maybe it’s naive, but we hope people enjoy being outside and documenting wildlife or identifying other’s observations because they find it rewarding in and of itself, and not for extrinsic motivations. So it is unlikely there will ever be badges or trophies on iNat. One reason we made Seek is to allow for a bit more gamification in something akin to iNat, but isn’t directly about contributing to public data.