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This is just what I did and used. Your mileage may vary. I'm well aware that with the right settings you can idle your way to this achievement. No judgement if you choose to do that but I didn't so here's how it went.

TL:DR
Rod - Horizon Caster
Hook/Tackle - Deep Glidebait
Zone - Icewater Sea
Map - Safety Cove
Location - I parked the Coastal Rambler one boat length away from the far right of the map, facing to the right (so I was fishing to the left)
Time of day - Dusk (as per the Log Book)

Details
I wasn't even looking for the big boy when he showed up. I just wanted money to buy stuff from Rusty. By the time I spotted him I'd already fished the rest of the XXL King Salmon out of the water so it was easy to grab his attention. XXL King Salmon are between 60lb and 126lb with the Trophy Weight threshold set at 94lb. The one I caught that triggered the achievement was exactly 126lb so I suspect it to be a unique fish just for the achievement.
A fully upgraded Horizon Caster is only rated for 48lb which is obviously why I lost him twice. The Grizzly Pole is rated for 54lb but that's still less than half of the fish I caught and the Horizon Caster has another 20' on the line length which was definitely useful as that damn fish ran me ragged all over the place!
If he does break free of your hook then reel it closer to your boat before you hook him again. No point starting from the limit of your line!
I used a combination of reeling until he started fighting hard (when you hear the reel clicking faster and higher pitched) then backing off, and trying to pre-empt him fighting hard by backing off before he did. I don't think there's a difference between the two approaches or if there is, I couldn't tell. I think persistence, more than anything else, is what landed him in the end.
The 126lb King Salmon gave me 1260 coins which is the highest single catch I've seen by a big margin and may be the highest in the game so this is obviously best tackled (hu-huh) while you still have things to buy.