When you exit the cave, you will have to go and talk to Agent Willis next. Fast travel to Amanaki Outpost and you'll call him. It turns out that Willis is leaving and is willing to drop you off over the southern island, but his plane is leaving shortly with or without you. If you have the Rust Yard outpost taken, fast travel to it, but if you don't, get on the quad and start hauling butt.
You have 5 minutes to get to the airport before Willis' plane takes off. Once you get close enough, the timer will stop and when you get closer still, Willis will call you and say that the pirates are attacking him. His health appears on top, so hurry up to the airstrip and take out all of the pirates that are there. When all have been killed, Willis explains he needs to do some repairs on the plane before you can take off.
Of course, the pirates aren't going to just wait and will continue their attack, so you need to protect Willis while he's repairing. A bar will start to fill up at the top of the screen, which is Willis repairing the plane. If the pirates attack him, he will stop working and the bar will stop moving, so make sure this doesn't happen.
The first wave of enemies, which mostly consists of a few normal enemies and knife-wielding ones, will come from the south. The second wave will come from the west, consisting of mostly regular enemies and a Heavy Gunner at the end. Some Machine Gunner trucks and normal enemies will come in from the west for the third wave.
The last wave will have enemies coming from the south and west, including a few Heavy Gunners and normal enemies. There is a stationary machine gun right next to the plane, which can be used for a few enemies, as they start coming from the south first. Once all of the enemies are dead, go to where Willis is and you'll get in the plane. When you jump out of the plane, the next mission will begin.
