After unlocking the fishing rod, you will see green rings (and fish) within bodies of water in the park. Find and access half of these in the park to unlock this achievement.
You don't need to fish in the traditional sense, so spamming RT whilst near the body is water works.
Some fishing spots will be checked off during fetch quests, others will need to be hunted.
TL;DR - equip rod and spam RT near any body of water you see within the park