We will be using journey mode to complete this as efficiently as possible. I would recommend using the "Journey Workshop" found in the Steam workshop. Subscribe to it and import the world in game.

1. Find the NPC section and see which fish the Angler NPC is requesting and stop time. This ensures the quest fish doesn't change.
   
2. Use a bed to set your spawn point near the Angler NPC. This is so you won't have to run back every time.
   
3. Go back and find the quest fish under the fishing section to research. This will allow us to duplicate the fish.
   
4. Duplicate the quest fish and fill your entire inventory with it. This will save time and stop you from duplicating it individually every time.

As many of you know, only 1 character can complete 1 fishing quest for each Terraria day. But you can bypass this by speeding up time or even creating a new character for each quest, this is not very efficient. Instead I found that the game only checks to see if the character name has completed the quest. By changing the name of your character before reentering the world, you are able to keep your spawn and inventory while still being able to complete the quest. I would recommend renaming your character to how many quests you have completed. For example: If I completed 5 fishing quests, I would rename my character "5".