Ruler of the Seas, how to do it?

In general, I think achievements such as those were designed to only be achievable through multiple playthroughs.

In any case, I think the idea to abuse barbarians in an archipelago map is good, just make sure that:

1. You get the honor social policy so that you're always aware where encampments are.
2. You don't destroy the encampments - leave them alive, and "camp" them by placing a ship nearby and destroying anything that spawns immediately.
3. Play with few opponents, if you can - barbarians only spawn (relatively) far from claimed territory, so you want as much of the map as possible to remain clear.
4. It's good that you play with slower pacing - it means there are more turns in which you already have powerful hunting units than when starting many new games.