In Biomutant, the Oxygen Suit is one of four armor sets designed to keep the player alive in unique hazard zones. The Oxygen Suit in particular will keep you alive in Hypoxia zones, which are pretty common in the dead zone area of the game.
That said, if you want to get the Oxygen suit, you will first need to head on over to Pingdish 11H to start the Pindish quest. In short, you will need to solve a satellite puzzle where you will need to align them with various singles when you arrive at Pingdish. After you do this, the game will reveal the location of the Oxygen suit on the map, which will be at Bangshelter 11.
At this location, you will find a ton of enemies, and you will need to clear them to get inside the building. However, that is not the only problem you will face. Bangshelter 11 is located in an extremely hot area, so you will need to increase your resistance to heat in order to survive in it.
You can do this by either equipping armor with high heat resistance or by increasing your heat resistance through bio points. We recommend doing the armor route as it is far easier and will save your bio points. That being said, once you got decent resistance, you will be safe to head into the area and find your new oxygen suit.
Start by clearing the enemies around the building and then head inside and make your way to a set of stairs. These stairs will lead you down to the final area in the building on the left side of this room, and you will find the oxygen armor.