The best way to get this quest completed is to go into the team rumble game mode. When you land, scavenge for any explosive weapons you can get your hands on and save them until the storm circle is small, as that is when the opposing team will be bunched up. Remember if you are eliminated in team rumble you keep your weapons so don't be afraid to eliminate yourself to take out another player.

There is a location where you can buy an epic rocket launcher from Splode in team rumble. The location is marked on the map below.

Map credit to fortnite.gg