This is a grind UNLESS you want to take the easy way:
*** Spoiler - click to reveal ***1. New Small World with a decent geared character/
2. Build 2 Small NPC rooms at spawn, with a chest.
3. Run to Ocean, find Angler, talk to him.
4. Fish for his fish of the day, then deposit it in the chest you made earlier.
5. Save world and quit.
6. Go to you Terraria Worlds save files (My Documents, My Games, Terraria, Worlds) and copy that world to your desktop.
7. Launch Terraria, hand in the quest.
8. Delete that world in the Worlds folder, copy the one on the desktop, paste it in the worlds folder.
9. Rinse and repeat.
This works because the quest data is stored on the character, not the world.
You don't need to keep closing Terraria either, just change the worlds from the main menu.
Takes about 30+ minutes of copying and pasting, but it's better than grinding it out.
I finished Terraria 4 times, and only had completed 50 fishing quests; then I used this method.
Good luck, Have fun.