As you discover near areas, be sure to talk to the Piscine Researcher in each one and complete the delivery requests he gives you, all of which involve fishing for some native critter. If you've completed all the other delivery requests for the Piscine Researcher (Ancient Forest, Wildspire Waste, Coral Highlands, Rotten Vale, Elder's Recess) and you see him again in the Rotten Vale, go pay him a visit. You'll find him along the eastern end of AREA 9, and when you talk to him he'll ask you to catch one final fish, starting the delivery request Research Help: Capture the Ancient.
You won't find this creature in the Rotten Vale, but amusingly enough, you can find one where you may have caught the last fish (the Platinumfish). Travel to the Eastern Camp (AREA 8) in the Elder's Recess and check out the fish-filled pool to the east, where, along the northern end of the pool, you may find the fish you're looking for. You'll know it if it's there, as it's rather large and has bright blue spots on it, although it can be somewhat far out to the north, possibly obscured by crystals. Catch this prehistoric fish, this Petricanths, to earn this trophy/achievement.