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Mutations that increase survivability help boatloads. I.E, euphoria, gamma guts, throne butt, hammerhead (to make immediate cover), impact wrists (can help with swarms of enemies and combos well with throne butt), scarier face, boiling veins and of course generally good mutations to have in any situation like trigger fingers and long arms.

Another note, you should want to get a golden wrench on melting as it makes getting this achievement much easier as deflecting projectiles and 1-shotting a lot of small enemies is a blessing.