The Beast of Brewer's Beacon

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A Salty stalwart is the acting guildmaster Sisipu, but today she seems distinctly distrait.

— In-game description

Rewards

See also: Big Fishing

Head to Cape Westwind (Aetheryte: Western Thanalan - Horizon) with plenty of bait (preferably Lugworm as noted in the quest, since you'll only catch the Merlthor Goby you need) with decent equipment. The rest is up to a lot of patience since you'll need two large-sized catches in succession to even get a chance to catch the Titanic Sawfish, and both mooches have a fairly good chance of catching a Silver Shark instead of the sawfish. The Titanic Sawtooth bites in Clear Skies from 9 AM to 3 PM Eorzea Time.
Head to The Brewer's Beacon (X:30.0, X:30.8) in Western La Noscea (Aetheryte: Swiftperch) with some Yumizuno. Since it's a lure rather than bait, 3 or so should suffice. Navigator's Brand has different requirements instead of the double mooch: A gathering rating of at least 290, and can only be caught between 9 AM and 2 PM Eorzea Time during Clear Skies or Fair Skies.

A Salty stalwart is the acting guildmaster Sisipu, but today she seems distinctly distrait.

Her tart tongue reasserting itself, Sisipu urges you towards Fisherman's Bottom, where Wawalago awaits you with a distinguished visitor.

Wawalago and Ascelyn bend your ear until you can hardly stand straight─such is scholarship. All you need to note is that Wawalago needs a titanic sawfish from you. Take a lugworm to Cape Westwind to catch a Merlthor goby, then perform fishwheeling to net a wahoo. Another round of fishwheeling─or mooching, if you must─will allow you to get your hands on a titanic sawfish.

You present Wawalago with a titanic sawfish, and faced with incontrovertible evidence of your prowess, the guildmaster reveals that an Old One called the Navigator's brand lurks off the coast of the Brewer's Beacon, and can be caught using a yumizuno. Heed his gory tale well and equip yourself with care. Without a high gathering value, you will lose this beast ere you can raise it out of the water.

Wawalago regards the Navigator's brand with naked hunger, but has the wherewithal to officially recognize you as a fisher with skill enough to capture an Old One, if such a need were to arise. The guildmaster also reminds you that Eorzea is apparently full of big fish for a self-improving fisher to hone his skill on. Word is that rare fish will fetch a handsome price in equipment at Revenant's Toll, unless you prefer to consume several dozen servings of a lemon herb Old One on a bed of spinach.