you must completely upgrade at least one of your various weapons.
Upgrade kits can be found all over Talos 1, most frequently inside of the different Security Stations. You probably won't need to worry about searching for specific kits. You can even find the plans needed to fabricate kits at a Fabricator, either from the Repair Bay in the Hardware Labs or you can download the plan from Sarah Elazar's computer in the Crew Quarters. A single Upgrade kit costs 3 Mineral and 3 Synthetic materials to create.
However, you will need to fully upgrade the Gunsmith or Lab Tech abilities in the Engineer Mod tree to fully upgrade a weapon.
Once you have at least one completely upgraded weapon you will have met the requirements.