Before fishing always make a hard save as a just in case. That way you can always reload instead of taken losses in special lure's. The key here is patience. Follow the prompts, always directing your rod in the appropriate direction. And if you feel your controller vibrating wildly, DO NOT REEL, stop reeling the moment the tentsion promps as well to avoid risk of your line getting more damaged. You should only reel when you are correctly leading the fish with your rod and there is very little (or no) vibration. Found the best approach when reeling is to tap the R2 button repeatedly or in pauses, rather than holding it down. That way, you run a lesser risk of damaging your line when the fish suddenly flips its direction. It will take a long time, but eventually you will haul in the monster fishes.
Lost Lure's
If you where like me and failed to remember to make a save before fishing.....then loosing the one lure the Knife T. Tonberry that you get as a reward for the first fishing quest found at Neeglyss Pond, that you can't buy or worse case have no clue where you lost it. Ease your mind there is a way to get it back without having to restart your game, cut your losses or find it in a old save. Refer to the video below to acquire a new one. It does work and I got my lure back after 4 trys.
How to Find these Items
ONE OF A KIND
Tranquily Rod: Is a reward for the Final Fishing quest at Galdin Quay (best rod in game)
The Howling Gust Rod: Reward for fishing in the Moogle Chocobo Carnival.
Air Stagger Rod: You get this when you buy the DLC "Angler Set"
Llymlaen Reel: The players have to give 85,000 medals by going to the arena called Totomostro in Altissia. Not really a OOAK but if your not into gambling it can be a "hassel" to get. (Best Reel in game)
The Albieo Reel: Reward for fishing in the Moogle Chocobo Carnival.
Fomalhaut Reel: You get this when you buy the DLC "Angler Set"
Big Blaze Bahamut Lure: Reward for the "tour" quest you acquire by resting at the camo near the Vesperpool-East Bank prompting Gladiolus Quest (listed below in quests)
Knife T. Tonberry lure: Reward for the first fishing quest found at Neeglyss Pond.
Big Master Typhon lure: The players have to give 45,000 medals by going to the arena called Totomostro in Altissia. Not really a OOAK but if your not into gambling it can be a "hassel" to get.
Tinselred Chocobo lure: Reward for fishing in the Moogle Chocobo Carnival.
Mog Rank: Rubygold Moogi: Reward for the finishing in the moogle Chocobo Carnival
Ranker Tonberry: Unsure where to get it other then doing the trick with lost lure's only this time at the forgotten pool fishing spot. Save before picking up the blue drop, if it is not the lure reload save and keep trying.
Tidal Might Leviathan: You get this when you buy the DLC "Angler Set"