Note: According to Hurricane Ham, these achievements will not unlock in No Sweat mode.
To unlock this, you need to do the following beforehand, otherwise you will struggle.
1: Build the Shrine for the Idol statues.
2: Find the Pipe or buy it from Lost and Found.
3: Build the Distillery, as this will make your job a whole lot easier.
4: Equip your preferred choice of weapons. I went with fully upgraded Fire Bellows and Calamity Cannon, along with Grenades. But go with what you feel is suitable to your play style.
5: Level up as much as you can first. I unlocked this at level 6. This allows you to equip more items from the distillery.
This will appear at the bottom of the Bastion hub.
Now equip 5 or 10 Idols and start the Who Knows Where via the Pipe. Then survive each Wave/Reflection. The Idols make it a lot harder, but the bonus is you gain XP and Shard in 5% increments for each one selected.
To equip all 10 Idols, you must first complete the story once to unlock Roathus and Olak.
Bit of advice, head to the distillery to add the following for some help.
Hearty Punch
Bastion Bourbon
Werewhiskey
Lunkhead Liqueur
Bull Brandy
Leechade
If the guide needs any more information added, let me know.