My edits/suggestions in bold:
Scene 1: You don't need to say "Scene 1." And also you need to say EXT OR INT. IE: EXT. ALLEY WAY - NIGHT
<Angel, Illyria, Spike, and Gunn are shown from behind as an army of monsters face them. The camera pulls back to the street in front of the Hyperion, revealing Connor racing to the second story window as the cries from the monsters grow louder. A second camera shows Connor from behind, calling for his dad as the four warriors leave his sight.>
Even though we know what the characters look like, since this is a either a pilot or a movie script, you need to describe the characters. Also, the camera shots aren't needed unless it is a production script and you need to describe the space, but do it simple. And the <><><><>aren't needed.
Connor: Dad!
<Connor turns and runs to the stairs. He hits the bottom step and gets stopped just before the door. A hand pulls him back against the wall.> Like I said before, the <> aren't needed, so I won't say it again. Plus the room needs to be described.
Kent: You’re not ready for this yet. Who is Kent? You need to describe him
<Connor pushes his arms away>
Connor: My dad is out there. I have to help.
Kent: This is his fight, not yours.
<The camera pans back, showing a legion of monsters running wild through the streets. Two of them head through the doors. Connor recognizes the monsters, as he is hit with a flash back of Quor’toth.>
<The scenery is rocky, with no foliage in sight. Holtz arises from a fallen monster, facing Connor in his animal skin garb.>
Don't need to say "Connor recognizes the monsters, as he is hit with...." Just say "A legion of monsters run wild through the streets as two of them head through the doors."
CUT TO:
EXT. ROCKY MOUNTAINS - DAY
Then describe the mountains, Holtz, the monster, what happens, etc.
Holtz: You must show no mercy with these beasts. You must not hesitate for one moment. You cannot think, you can only act.
<In the hotel, one of the monsters, goes at Kent and takes him to the side. The other goes after Connor, tossing him into the weapons chest. The camera cuts to Connor arises, now in the flashback.>
Holtz: Right. Left. Block.
<Connor follows Holtz’s directions, as he fights against a monster that is exactly the same as the one he’s fighting. The camera switches to the demon, who has fallen to its knees, back in the hotel. The camera switches back to Connor in Quor’toth.>
Holtz: Finish him.
<The camera is back in the hotel, as Connor reaches out to the monsters head and snaps it. He grabs a piece of glass from the broken cabinet and throws it at the second monster, which was straddling Kent. The camera shows Kent’s vantage point, as the monster falls off to the side with a piece of glass lodged in its head. Connor pulls the monsters off and pulls Kent up. They head to the door.>
Connor: Want to tell me what I’m not ready for.
<Connor opens the door. The streets are in flames, blood is running down the side of the street with the rain. Opening credits roll.>
When you are doing the flashbacks, you need to have CUT TO and EXT/INT slug lines.
I am too tired to go through the whole thing, but you have something great on your hands here. The only problems are the format and describing the scenes/characters. The dialogue is very good, especially Connor. Most of the stuff he says sounds just like the way he would say it, you did a very good job at it.
If you have anymore questions, just ask.
