Oh, my bad! The Ice Fishing achievement thinks it's the Mountain Fishing achievement, and pretends to be achieved in the menu if you have gotten the Mountain Fishing one!
This should get fixed in the next patch. Also, I
think you can get the trophy in the current version by getting all the fishes, as the actual trophy check shouldn't be affected.
Additonally: Thanks
@HexZyle for providing me with the save file to investigate