Before going to actual solution I'd like to mention that I usually don't post solutions before I unlock them myself, though for this achievement I thought it might help if I already posted some of my findings.
This achievement requires you to gather 500 Thorium
(Or at least it seems like that if the achievement description is correct). Thorium is a resource locked until your Headquarter is upgraded towards level 16. You have oil and steel unlocked from the start. Polymer unlocks at level 10 and then thorium at level 16.
You will need to get a lot of resources for this, and besides you will need to upgrade a lot of other buildings as well, as for some of the levels I had to upgrade other buildings to a specific level as well. It will take quite a while to get this achievement, very much in contrast to the other achievements which are a breeze. I'm currently at Headquarters level 8 after about 2 hours of gameplay. Though time needed for upgrading one level increases with each level that I add to the HQ.
- I'm currently constantly doing the renegades. I've built quite a decent army and I get quite some boosters for resources from attacking the renegades.
- Using the boosters also helps a lot. Click your resources in the top right and there you can use boosters which you have acquired one way or another.
- I would also advice to complete as many quests as possible as they also give you resources and besides, you will also have to upgrade some of the buildings as requirement for upgrading your HQ.
For the actual building time:
Join a faction (there is a TA faction, though almost full at the time of writing). You can request help by building stuff, which reduces the time needed for it to finish.
- Besides, the boosters which decrease building time also help out a lot.
- Below your HQ you can add pieces of gear to your commander to gain some perks.
- It'll cost you about 80 dollar if you want to get this out of the way quickly.
-Upgrading to level 11 takes around 11 hours.
- The upgrade to level 16 costs 4.2 million steel, 4.2 million oil and 2 million polymer.
Feel free to add info if you have extra tips, let me know what I can improve on and I will try to add more info as I progress towards level 16.