Rare fish appear as red shadows. The following list includes all of them and what to catch them with.

Kanto Area
Oodeo Bay: Red Rockfish (Sea Lice)
Guuzenji Lake: Rage Trout (Stone Fly)
Koarai Beach: Rainbow Eel (Baby Lonia or Sea Lure worm)
Katsumura Bay: Sea Goblin (Broken Ladle)

Chubu Area
Hamami Lake: Star Eel (Baby Lonia or Cuttlefish)
Nagaha River: Rage Trout (Stone Fly)
Manaka Lake: Pink Bass (Stone Fly)
Noyama Bay: Midnight Bream (Straw Worm)

Kansai Area
Myoujin Straits: Sunrise Fish (Spoon Worm)
Godanheki Cave: Giant school of red fish (Sea Lure worm)
Hiwa Lake: Pink Bass (Stone Fly)
Chamo River: Rage Trout (Stone Fly)

Chugoku Area
Shikane beach: Fat Sea Bass (Cuttlefish)
Ootori Coast: Round Amberjack (Palolo Worm or Sea Lure S fish)
Isono Island: Midnight Bream (Palolo Worm, Straw Worm, or Prawn)
Fukuyobi Water: Devil Puffer (Possum Shrimp)

Shikoku Area
Urayama Dam: Rage Trout (Stone Fly)
Kosa Bay: Red Fish, Dragon Bonito (Prawn) Summer/Sunfish (Jellyfish) Summer (rare); Sunfish rare but not Red Fish.
Mikoto Bay: Puffer Trio (Baby Lonia)
Muwakai Offshore: Round Amberjack (Sea Lure worm)

Kyushu/Okinawa Area
Nagasaki Water: Mom In Law (Prawn)
Ookita Bay: Eye Rock Fish (Shore Crab); Winter: Ookita Horse Mackerel (Straw worm)
Hazakurajima Beach: Jumbo Parrotfish (Ghost Shrimp)
Chura ocean: Stone Puffer (Sea Lice)

Tohoku Area
Matsurgahara lake: Rage Trout (Doughball)
Monaka River: Manface Fish (Doughball or Frog)
Annri River: Water Imp (Cucumber)
Daimon Strait: Bluefin Tuna (Sea Lure worm)

Hokkaido Area
Ishihari River: Chum Salmon (Meal Worm)
Marimo Cape: Fat Sea Bass (Prawn)
Yakan Lake: Huchen (Fresh Lure Worm or Meal Worm)
Oohokku Ocean: Halibut (Sea Minnow)

Unknown Area
Rapuso Monument: Pirarucu (Freshwater set)
Blue Cave: Red Metal (Bolt)
Deppari Cape: Devil Shark (Raw meat)
Fish City: Whale Shark (Spear lure)