Make the beginner fishing rod with 10 Paldium fragments, 3 Pal Fluids, 8 Ingots, 8 Fiber. Approach a glowing spot in the water to fish.

Make the intermediate fishing rod with 30 Paldium fragments, 10 High Quality Pal Oil, 10 Cement, 30 Fiber. You can use this fishing rod to catch harder pals. Keep your eyes out for purple spots because they have rarer fish.

Make the advanced fishing rod with 30 Paldium fragments, 20 High Quality Pal Oil, 15 Pal Metal Ingots, 30 Carbon Fiber. This is the second best fishing rod and the last one you can get before needing to find a blueprint.

Head to the enemy base found north of the snowy mountain region. There you will find the depresso fishing rod recipe which is the best rod in the game. Craft that with High Quality Pal Oil x20,
Paldium Fragment x140,
Pal Metal Ingot x30,
Carbon Fiber x20,
Coralum Ingot x5.
Then get Whalaska and Whalaska Ignis for easier fishing and Jelliette for better fishing drops. Then find very purple fishing spots and you will have a decent chance to find a lunker.