As you progress through the game's story, you will begin unlocking elemental weapons automatically, or will gain modifications to change the properties of weapons you already have. By the time you are finished on planet Monarch, you should have all 5 weapon damage types, or will unlock them shortly after.
The types are as follows;
- Kinetic (Normal)
Once you have all 5, equip 4 of them into your active slots, and find an enemy, hitting them with all 4 weapons. Go to your inventory and swap out the last type, hitting them again and killing them to gain this.