You must complete the first five levels and then beat the boss, and enter the first portal elevator you see.
There is a second hidden portal elevator in the same room that takes you further to a different boss level, do not enter this one or you will miss out on this achievement.
To make the game easier: use the Tooyoungtodie perk, this increases your armour, loot drops XP and weapon damage, to unlock this take 4000 damage, you can see your progress by clicking on the weapon if you have not yet unlocked it. Always remember to use the best weapon you have unlocked and stick with a mod which doing lots of damage, rather than switching just because one is available.
Personally I found changing the game mode to DICE ROLLWas really helpful, It gave great loot drops, weapon mods, and health drops. Each time you enter a new doorway the dice is rolled and it comes up on screen what the pro or the con is. Give it a go I found it awesome.
A tip for the final boss, as it is always the same boss (Gumball Machine) you will need to shoot the glowing globe above it to uncover its metal shield, which is when you can shoot and damage the boss for a small moment before the shields go back up again, repeat until the boss is dead, and watch out for the spinning drills on the ground and turrets from the ceiling.