You need 50 kills with explosive weapons in ranked or player matches. This is cumulative so every kill will count towards the 50. The weapons that can be used to kill enemies and count towards this are:
Unfortunately you only spawn with 2 of each. This means you can’t spawn camp indefinitely with your C4.
Of course you can do this with a friend. I recommend setting the time limit to 20 minutes and setting the game to Attack and Defend on Calypso Casino. This gives you unlimited kills and 20 minutes to get as many as possible. Set yourself to attack and your friend to defend. Create a class with frags and C4. Always have your friend spawn in the Kemo room.
When you run out of frags and C4 then allow your friend to kill you and then zip line down through the main window on the roof into the middle of the large casino area. This will bring you right next to him, then return to killing him.