Here is the full list of all 12 Reel Fishing: Master's Challenge trophies - there are 8 bronze, 3 silver and 1 gold.
Story: Complete Chapter 1
Story: Complete Chapter 2
Story: Complete Chapter 3
Story: Complete Chapter 4
Story: Complete Last Chapter
Got all the lures and baits.
It's just a bronze, but it's out of sight
Got all the aquarium items.
Received all As in missions.
Caught 300 fish.
Got all the items.
Caught all fish in all sizes.