This requires you to bring 10 weapon blueprints to the Collector. You do not need to spend cells on unlocking the weapons, bringing the blueprints is all that is necessary. Blueprints are random drops from killing enemies.
You can check your progress towards this achievement in the Weapons section of the Progress screen that you can see by talking to the character next to the Daily Challenge door at the start of the game. The achievement will unlock when you bring the 10th weapon blueprint to the Collector.