The First Descendant

I'm going to put the guide for the weapon and descendant extension achievements in one guide since it's almost identical on how they're obtained.

You can extend a weapon or descendent's module capacity by going to their module selection screen and going to "Module additional settings" on the right. Click on that and choose "Max capacity up". You need an energy activator in order to be able to do this. You can only do this once per descendant or weapon. Following this guide you should be able to get the achievement for both extending a special weapon and extending a descendant.

You can get 2 energy activators for free while working through the rest of the achievements but there's also two other methods.

First free one: Reaching level 40 on any descendant for the first time
Second free one: Complete the normal difficulty story by completing all of the 8 main areas finishing off in the Fortress.

The other 2 Methods:
First method :Buy them from the store for $24 (USD) in the premium store a piece. So $48 for both achievements.
Second method: Gather the resources and craft them. By getting this far you should have completed the story so you should have the ability to find and gather every material type in the game. When looking at what you need to craft one of these items you can press on any material type you need and it will tell you where to find it. The higher lvl the zone the harder it is to fight for but the more of the same resource it is likely to give you. Especially on hard mode.

At the weapon adjustment table you're also able to re-roll weapons (This also applies to weapons found while playing the game) that have increased consumables drop rate. This will help increase how many resources you get.

Not sure why this is being downvoted since it tells you how to do it, the only methods of obtaining the resource for free, and every method for gaining them.