Vault-Tec ArchitectG 10

Vault-Tec Architect G10:
Build 25 rooms

The best way I've found to get this achievement is to build extra power rooms and merge them. I did this because it doesn't require any resources other than caps to do and doesn't hinder you in terms of production in any way. Plus if you're current power room is quick enough you can take advantage of the added storage and stockpile some of the energy for later need.

I have a guide video showing this method here if you need more clarification:

https://www.youtube.com/watch?v=TQAjoCmFxx4