Quickly switch to Armor and Blade after the cinematic ends. Having Infected Vision will help. Stay away from the Boss until he starts to jump. After he lands, attack him with an Air Blade Slash. He will become stunned after a few good hits. Grab him and repeatedly punch. If you are taken down to critical level, use a Devastator move to stun him.
As soon as the battle begins use your armor power and hook power. Immediately begin to use one of the following tactics.

Tactic 1
Keep him locked on. Hold [Jump] for a moment to get reasonable air. As soon as you jump, hold [Attack] button and allow it to fully charge. Then, immediately repeat. This should take four stuns to kill him. Do not bother disguising as the military will barely bother with you.

The first stun
The Supreme Hunter will be stunned very quickly from this. As soon as you are locked onto him and press [Grab], you should hook onto him and immediately be able to begin punching him. Instead of button bashing, press [Attack] at an easier rate than you normally would. It will register more and you will attack quicker. After the first stun, which comes very quickly in the battle, he will finally get the chance to use most of his attacks out on you.

His attacks

Normal Attack: His normal attack is usually swiping at you with his fists and will fling you into the air. These are very easy to dodge. If you are having trouble, try jumping then air dashing away or over him.

Throwing: Around the battle area are several explosive props which he will pick up and throw at you if you are far away. This is rare however, and he will usually miss.

Spike Attack: When he uses his attack, it is a very good idea to jump and double air dash away from him as much as possible. As soon as the spikes have shown themselves, it is useful to run at him quickly and get a few good charged slashes into him with your blade. You should not need to do this until after stun two.

Devastator: This is very easy to dodge. He will stand still and begin to spasm a bit before he unleashes his Devastator. Do not stand close to him during this time, as he can unleash an instant kill on you even when wearing armor. Instead, lock onto him and air dash around him in a circular radius until the main large tentacles have tried to hit you. Once they have missed (there are about three or four of them), find a spot clear of the large tentacles and change to blade power. Begin swiping at him with slightly charged blade attacks. You should be able to get your first hits into him while the tentacles are still moving out and not retracting. You can also get hurt while they are retracting; try not to run into them.

Repeat "Tactic 1" and counter his Devastators when you can. You will eventually stun him for a second time and you should encounter a cinematic during or slightly after the second stun. After the cinematic, you will realize that you have a time limit to kill him. Do not worry about it. Just repeat the first tactic and he will eventually die. You should not need to use "Tactic 2" unless playing on Hard mode or running low on time.

Tactic 2
Wait for the Supreme Hunter to land after a jump and slash him from behind with a few slightly charged blade attacks. As he turns to attack you, jump and air dash over him. You may choose to aerial attack him with a kick or slash him and then jump away. This will lower his health quickly, combined with attacking him during Devastators and spike attacks. This is advised only if you are really running low on time and have just finished stunning and hitting him.
Depending on whether you are still using "Tactic 1" (recommended), you should be able to quickly finish off the hunter within two more stuns. There are four stuns in total. Each stun should take away about 25% of his life under the Medium difficulty setting. If you are using the blade tactic, you will probably encounter him for longer and may get less stuns on him.

Healing
You should not need to heal before the cinematic. However, if you do get hurt badly during the second half and there are no people to consume, either stay with "Tactic 1" and jump kick him, or run to the part of the ship with the turrets (the tower object) and jump behind it into the water. As you jump back out, press Forward against the ship and you should hit the ship while coming back up and fall back into the water. Try to press [Grab] onto the side of the ship and heal there if possible. The Supreme Hunter should not be able to hurt you there. Just remember you have a time limit.