No matter what, this is a grind. However, I can offer what I found to be the most efficient and quick way to get this done.
First, I saved this achievement for last because fishing is relatively useless in the game. Add to that, you'll want the excellent fishing rod that I was able to buy from the fisherman after I traded him all the fish I'd caught going for the 15 different types.
Take your excellent rod and go to the fishing spot near the quarry - it's east and a little south of the cabin along the river, on the east side. From there, choose no bait, and throw the line in the first third of the bar for the nearest option.
At this point, if the fish isn't 100% the same every time, it's too close to matter. I found that counting out loud, "one thousand one, one thousand two, one thousand three," and so on got the fish to bite on the bait between six and seven. You can count however you'd like; the point is, the fish bites consistently so you're not strained watching for the small movement and short window (especially in rain or fog).
Once the fish bites and the mini-game pops up, press and hold A, and... that's it. The fish will follow the same movement pattern every time, and I found that with no previous bar-filling, with the top rod the fish was caught every time if you just hold the button and keep the bar at the top of the gauge. This way, you're also using minimal energy to catch each fish which allows you to get more.
Once you've caught all the fish you can at a time, this spot is great because you can walk to the quarry cabin and sleep/save there, and then start all over again.
To summarize - best rod, consistent timing, hold down A to catch the fish every time it's hooked, and save in the nearby cabin. Enjoy.