Destroy All Humans!

To unlock this, you must unlock one branch for a weapon or ability. The weapons have 2 branches while abilities have one. You will need DNA to purchase each upgrade of the branch and will also have to progress through the missions to unlock said upgrade. Once you have purchased an entire branch, the achievement will pop

Shields for yourself is the easiest, as there are only three levels to select, and you can do it by the end of the drive in level. (Shields for your ship is also only three, but will take at least two levels longer.)

Here is my 100% Achievement guide and full walkthrough so you don't miss a thing.

This is unlocked for fully upgrading one of your weapons or abilities.
To do this, you need to collect DNA which is done through various things.
Completing missions, side missions, collecting furon probes but more popular is to mash the button with an Alive enemy.
That will automatically pop out his brain for you to collect and get some DNA.

As for what weapons to upgrade.. the zap o matic is a good one as we need it for the final boss anyway and is cheap enough.

Go to 2:21:15 in my part 1 video to see where and how to unlock this

Hope this helps!

Part 1

Part 2