Chiming in at last!
First, off, I enjoyed this first chapter in your novel. Thanks for sharing it with us. It reminded me a lot of Mistborn due to the post-apocalyptic world, and the fact that humans gain power and strength through gems. (Although in Mistborn it was metal, of course). It also had a strong anime feel to it. As a matter of fact, when I logged on just now to reply here, I saw your avatar is Cloud from FFVII. I can totally see that connection, especially with having a big dark-skinned companion.
Anyway, IMO, mixing Mistborn and Final Fantasy isn't a bad thing at all. :-D
Several people on this thread have commented on your typos and repeated words already. Those are easily fixed, and I'm sure you'll get them. All I'd add to those suggestions is that you may want to do a general Thesaurus pass and see if you can find ways to up the level of description and word usage. It's not that what you have isn't good, I can just tell this is basically a first draft and I have a strong feeling you know you could take it a notch up.
The chapter started off pretty well. You picked a great moment to start the story. I love the idea of the first moments being literally on the edge of a cliff (errr... wall). I also loved the imagery of the sun rising glimmering over the city just as they arrive at the top of the tower.
With regards to that first part of the chapter, I agree with the person who posted and said that it felt odd for one of the characters to remove their gloves while hanging onto the wall.
Put me in the camp that was confused by "heartcrystals", "crystalhearts", and simply "crystals". By the end of the chapter, I got the difference, and I think I understnad. So it might be okay afterall. But frankly, it frustrated me as I was reading, and took me about 12 pages to feel comfortable with those terms.
The fight on the wall didn't work for me at all for a few reasons. First, few actual actions were described. You wrote:
Dantes was raw power. His sword was built like he was; strong, heavy, thick. It was made for one thing; to be brought to bear on the enemy with as much force as possible.
Preferably lethal force.
But where Dantes epitomized strength and brutal crushing force, Aermyst epitomized skill. He preferred grace to power. He too mirrored his blade; slender. Flexible. Quick. The two were counterweights to each other, perfectly balanced. They were equals.
Show us. Don't tell. Let's see some action verbs!
The above paragraph told us things we already knew.
The second reason the fight didn't work for me is that it served no purpose in the story that I could tell. It didn't really tell us anything about the characters, other than they were proficient with swords. We already knew they could jump and move far better than normal people. And it didn't really advance the plot itself'; it didn't have them fall into any traps, or reveal new skills, or show us any character moments. Honestly, if you cut the whole fight entirely, nothing would be missed.
That said, I LOVE the line:
This city was theirs.
For this paragraph from page 10:
Aermyst looked across at Dantes, keeping one eye on their surroundings. The two could not have been more physically different. While both were tall, Aermyst's fair skin contrasted with Dantes' dark ebony skin. The big man's black locks were tied in a queue at the shoulders, as opposed to Aermyst's fine, scarlet hair that came to his neck. Where Aermyst was knife-slender, Dantes was big as a boulder. The two had been friends for nearly fifteen years.
It seemed like you were trying to use this beat in the chapter as a good time to describe your characters. There was no need to. Every single bit of info in that paragraph except the last sentence were things we already knew. Perhaps consider using this moment in the chapter to give us a little more insight into those 15 years? Or their nature of their friendship? (By this point in the chapter, I was more interested in how they knew each other rather than what they looked like)
Also on page 10:
As they reached the edge of the ruined city, Aermyst drew his attention back to the task at hand.
What exactly IS the task at hand? They already got the crystals. You had not stated exactly where they were going. I felt like that sentence implied I (as the reader) should know where they were headed, and I did not.
RE: Ves. Eh. I wasn't convinved. He was pretty flat. At first he was described as being a man of few words. But shortly after that, he has veins popping and is yelling? Generally speaking, IMO anyway, people who yell and are self-centered like Ves aren't going to be men of few words. Men of few words are good listeners. And Ves is NOT a good listener. At least, it didn't seem like you intended him to be? If the anger is important to his character, then consider adding a little more build up before he pops.
Page 12... Dante tosses the crystals onto the table. This moment felt weird to me. The crystals had been described as soft and fragile things that were handled with such care earlier. Now he tosses them casually on the table? Consider clarifying.
Page 13:
Aermyst was more blunt. "Ves, you are bloody insane. "
There is no need to tell us he was blunt. The line of dialogue should convey that in and of itself.
Last thing... I get the sense that you have a great story you want to tell. More than just the action and magic. I get the sense that you want to tell a story about Aermyst and his struggles to find his own identify. That's great. I look forward to the themes and conflicts ahead which I assume you started to plant here in chapter 1.
Onto chapter 2!