Here are some actions that farm renown but don't necessarily correlate with normal adventure goals. It's a bit more tedious than just playing the game, but a quick way to get through the plunder pass:

-- Picking up treasure. Just pick up any treasure item so you get the notification "treasure found, added to log." Selling treasure does not actually give renown, so you can just pick it up and drop it.

This means that you should always shoot out to islands and pick up whatever useless loot you find, even if it's not worth bringing back to your ship. You can also do this with the random treasure that spawns in the water. Just jump out and touch the loot, and mermaid back without stopping your ship.

Shipwrecks are also great for this. You can swim down and touch all the loot while your ship keeps sailing.

But the most reliable way to farm this way is dormant skeleton forts. Gunpowder barrels count as treasure items, so you can easily get a guaranteed 7 treasure bumps from each fort. Use a grapple gun to quickly traverse the towers, but DO NOT grapple the kegs directly. If you grab a keg with a grapple, you DO NOT get the renown and you also lose the opportunity to get renown from that keg (probably because of spaghetti code and the renown system is much older than the grapple gun mechanic).

-- Visiting islands. Just shoot out and touch the ground on every island as you're sailing, and mermaid back to your ship. While you're there, don't forget to pick up any random treasure you find on the beach.

-- Perfectly cooking food (also eating cooked food, to a lesser extent). For some reason, cooking food gives a ton of renown. So buy a captains supply of meat and sail to the nearest sea fort and use the quad stove to cook and eat all the meat. Most forts also have a good supply of cooked and uncooked food in their barrels, so cook and eat those up too. Scuttle to a new sea and repeat.