Well, thanks to the tips in El's Extreme Anglin', combined with data found in the great Book of Thott, mixed with a whole lot of luck, I just became Salty.
I caught my first fish on October 16th, and tonight, November 11th, 26 days later, I just completed the One That Didn't Get Away achievement to get the title.
And now that I've used up all of my luck on getting this title (that's how it works, right?), I'm off to try completing the rest of the achievements. The only other major one I've finished is the Sea Turtle. I see many hours ahead of staring at that damned bobber.