(Possible minor spoilers ahead.. spoiler tags used for the most egregious)
Completing three trips to who knows where is the requirement for this achievement. They begin through the lamp, cooking pot and bedroll respectively. The final final one becomes available shortly after you get the following achievement:
The third trip is by far the hardest. This is the setup I used to finally beat the it after several attempts - all of which ended on the final wave/reflection.
Fire Bellows (sustainable fuel, napalm reservoir, modified intake, contoured grip, streamlined furnace)
Fang Repeater (speed clip, heavy bolts, hollowed chamber, reinforced piston, tracking critters)
Distillery (I was level 6 so had 6 slots): Hearty Punch, Bastion Bourbon, Werewhisky, Lifewine, Graver Gimlet, Leechade
Strategy for the third trip:
-Save your Snooze Darts (RT) for the 'ninja' Ura with swords. Hit them with the dart, then with the Fire Bellows and they should go down easily.
-Use shield extensively throughout (with LT). It blocks the laser turrets and the gun Ura very easily.
-When the birds spawn, try to get up close and use the Bellows. Keep moving around or you'll get hit.
-The 'beast' type monster that jumps up and down is usually only vulnerable from the back, but if you use the bellows it doesn't matter from which direction you fire on him. Wait for the jumps, then dodge.
-Leave your Black Tonic bottles on the ground until you have an empty spot for them. No point converting them to exp, you'll need them to get through the trip.
-The Napalm Reservoir upgrade for the bellows is vital as you can set the enemies on fire, then hide behind your shield and be protected while they take damage.
-Coming into the final wave/reflection you should ideally have full health, full tonics, and some healing potions. The tonics are probably the most important part.
-For this wave itself, try to stay around the edges of the map, behind the spike rocks on each side - then the poison dart Ura won't be able to hit you as easily. Take out the ninjas as soon as possible, use your black tonics but make sure you go for it fully and take them out once you've used a tonic. -It is very easy to get overwhelmed. Once you've dealt with the ninjas you have a bit of breathing room. Keep your shield up and take out the remaining Ura.
If you can complete the third trip (bedroll), the other two should be relatively straightforward. Use the same setup listed above and you should have no problems.
The achievement unlocks when you get back to the Bastion after completing your final trip.
Hope that's helpful, any questions post a comment below and I'll get back to you.