The Last Kids on Earth and the Staff of Doom

To those nearing the end-game and struggling with this achievement... bad news. Your game may be glitched!

Actual guide:
Make sure you have 10000 scraps/nuts/parts. At the town square, go to the tree house and click to enter. Click on "TREE HOUSE UPGRADES" and then hold . The achievement should unlock the moment you finish upgrading the tree house to level 2.

Glitch TL;DR:
If you do not have the option to upgrade the tree house early in the game, like immediately after the turret defense zombie wave, do not proceed with the game and consider starting a new game. Saves you the headache of almost completing the game to find out you're stuck.

Discovery/Speculation:
Not 100% sure if this is the reason, but when I started this game, I was button-mashing as often as it would let me skip through dialogue and skipping scenes. At one point early game you are at the tree house unlocking turrets, I believe if you upgrade your turrets prior to that first zombie wave round, your game may become glitched and your ability to upgrade the tree house gets locked. No matter what you do, there will be that lock on the tree house and you cannot upgrade. Unless someone discovers a workaround, you may be out of luck. To avoid this, consider just unlocking the 2 different turrets and continuing with the zombie game. Afterward, check if you can upgrade your tree house and you're in the clear.

Good luck and hope you find this before you try to complete a glitched game!