First off it's well worth saying this achievement is a little buggy. It took me a few goes along with a few other people. Some of the physics for moving animals are a little odd, I personally had a hog fly off the map when trying to put it onto the raft so be gentle. The animals also don't stick very well to the raft so you need to be well prepared. Before you begin make sure you're well fed and watered as there will be a little bit of waiting.
You need to have these animals on board during a storm -
2x Night Snakes
Your raft - I personally had a 3x1 raft, but if you have something bigger there's less chance of the animals falling off. It can be done on something smaller though with a bit of care. Make sure your raft has an anchor, sail and rudder and kill the following in this order-
Crabs - Easy to kill, they can store in your inventory for when you need them. Don't skin them.
Seagulls - Throw a spear into group of them or wait till one sits on a rock / tree. They only appear in the day, again, they can be stored.
are plentiful. Keep them in your inventory so they won't disappear and get them out when you need them.
For the next part we're going to use any island to 'farm' animals. Save then back out to the Main Menu > Cartographer > New Island > Animals Tab > Toggle to the wild boar setting to 2/2 and Night snake to 2/2. Apply the settings, back out and save, chose any name and any description and once done go to World Editor and 'Replace Island' on the island you want to replace, back out and save. Make sure your map is small with few trees and rocks to find the animals easier.
Sail to your custom island and pull your raft onto the shore and kill in the following order -
Night Snakes - Poke them with spears, if passive mode is on they can't hurt you. They appear thought the day / night contrary to their name. Kill them but use
to carry them to your raft. Put them right in the middle.
Boars - Best killed by poking them with a spear, use
to carry them to your raft. Put them in the middle. Don't skin them as they fall through your raft if you do.
Bats - We're leaving these till last as they're plentiful but there's a glitch where they disappear from your inventory if you leave the game or reload. Throw a spear into group of them or wait till one sits on a rock / tree. You can keep them in your inventory for now though.
So by now you should have 2 crabs,
2 seagulls and 2 bats
in your inventory. 2 boars and 2 night snakes on your raft. Carefully pull the raft out to sea and turn it around to the open ocean, it doesn't need to go out too far. Make sure there's no rocks, corals etc in front of you so when you're ready to go your raft won't get stuck. Stick your anchor on and keep an eye on your boars and snakes falling off, adjust them if necessary, once they seem stable enough throw the crabs,
seagulls and bats
into the middle of the raft. You will literally have a pile full of dead animals. As soon as it starts to rain, release your anchor and get sailing off into the sunset with your well earned achievement. It should pop up reasonably quickly into your journey.