This quest requires you to damage an opponent within 10 seconds of landing onto the island.

There are a couple of ways you can easily get this.

The first is to jump off the bus with a lot of other players. You will be able to see people jumping from the bus if you spin the camera around to face the back of the bus. Keep a lookout for someone falling for gliding close to you and follow them down. The strategy here is to drop in very close to them and hit them with your pickaxe as soon as you can.

The second is to follow the strategy outlined above but instead of dropping on top of another payer keep a look out for where some players land and the locations of floor loot that you can land on top of. There can be guns on top of roofs in some areas of the map. If you kept an eye on other players you should be able to shoot them and get some damage within 10 seconds.