Here is the full list of all 15 Fishing Paradiso achievements.
Hiroki enjoyed the beach chair.
You collected all the "Signs of Friendship."
Your friends tasted all of the restaurant's dishes.
You became friends with everyone.
You won the fishing competition.
You caught all the species of fish.
You caught a total of 1000 fish.
You maxed out a friend's Friend Level for the first time.
You met again with God Fish Martel.
You caught a fish that is at least 1000 cm big.
You caught a total of 300 fish.
You caught a fish that is at least 100 cm big.
Your house is now built.
You cleared your first main quest.
You maxed out all of the fishing abilities.