-( Story related, cannot be missed )-
The Gunslinger UFO is the second boss and the final level of the Desert Zone. It has three phases to it where it will change up its pattern of attack or increase the damage potential of its previous attacks. Go in on your first time actually trying to clear it, regardless of damage, so you can better prepare yourself for what it will bring up.
It takes six hits to clear the UFO, so be prepared for a challenging and somewhat lengthy fight, compared to the first and last of the UFO bosses. Prime focus would be to maintain the middle so you can make adjustments according to whatever attack it shifts into. The attacks that it can perform are:
* = Attacks that leave an opening after it is complete.
*1) It will move to one side, turn upside down, and start a strafing laser down onto the ground. Avoid the attack by placing yourself in the updraft (not hovering in it, but just standing on the platform). In later phases, it might adjust to doing this repeatedly by letting up, going further in the direction it was going, and then resuming. To counter this, be ready to use Pounce to get away and move to the other updraft.
2) It will turn onto its side and begin charging two lasers up towards you. Rush over to a vent and tap the Hover button to keep between the beams. After the first phase, it will send large pulses down the laser beams in a pattern (10, often up 2, down 2, and then a mixture between). Continue to tap the Hover button as necessary to avoid touching them and the other beam.
3) It will hover above the battlefield and extend its two arms. The tips will light up and it will proceed to fill the air with a volley of laser shots. In later phases, the number of bullets per shot or the actual size of the bullets will change to orbs. The same strategy for all three variations is to move as little as possible, only when you have to move out of the immediate way.
*4) Staying in one place, it will start to gather energy. This is a cue to immediate run over to where it was hovering, as it's going to jump over to the other side, turn sideways, and hit you with a wide laser beam. Jump into the updraft and ride it up to the top, staying there as your only safe spot. This is a mid- to late-phase run for the boss, so you won't have to worry about this pattern changing.
5) Combining both lasers while hovering in the middle, it will call in reinforcement Woolies. The amount of Woolies called in will increase over later phases. Be careful trying to jump onto them from above as you might be pushed upward into the UFO and get hit in the process.
*) In the last phase, he might actually combine 1 and then lead into 4, so be aware of the updrafts and how far you are, just to avoid getting hit with one jump left to go.
For the visual learners, this video shows what to expect when trying to clear it without dying: