You will need to catch 6 fish to score this achievement. Just as ComboChrist has mentioned this is much easier than in Far Cry 5 since you don't need bait anymore. The fishing rod is unlocked via perk.
You also get one perk point for every new fish you catch.
Here's all the fish you need to catch. Some of them have challenges associated with them, others do not.
Fish 1: Rainbow Trout
Fish 2: Bull Trout
Fish 3: Smallmouth Bass
Fish 4: Chinook Salmon
Fish 5: Largemouth Bass
Fish 6: Paddlefish Sturgeon
Here's a great guide to fishing in Far Cry 5 New Dawn from PowerPyx! Make sure to give him a thumbs up on YouTube, his guide videos are incredibly well done: