Here’s where to find the keycard to the vault, and where on The Rig it’s located.
Getting the keycard
When you exit the battle bus, look for The Rig on the left side of your map — it looks just like an oil rig, hard to miss. Drop down and land on the roof of one of the buildings. Grab a weapon and make sure you sneak around — there are loads of henchmen here, and they like to shoot on sight.
Walk to the center of The Rig and keep an eye out for TNTINA (pictured at the top of this post). TNTINA is the boss of The Rig, and you can identify her by her red shirt with a yellow grenade painted on it. She also carries a large bow — which you can use if you kill her. If you’re having trouble identifying TNTINA, she also has a crown icon above her head when you look at her.
When you find TNTINA, use your weapons to kill her. She will drop the Rig Keycard, which you need to open the vault. Pick it up, and jump off The Rig.
Where on The Rig is the vault?
With the Rig Keycard in your pocket, jump into the water under The Rig. Swim to the top right strut — the one right above the “R” in “Rig” on your mini-map. Since you have the keycard, you’ll have an icon pointing you in the direction of the vault. Walk around to the inside of the strut and place a staircase. Walk up and destroy the wall to your right. The gallery above should walk you through the steps.
Inside the strut, you’ll find a key reader and the vault. Scan your key to open the vault door. Inside, pick up all the loot you can hold, and use the porta-potty in the corner to teleport you to the nearby swamp in the mainland.