I have only read the first chapter but I have a couple of things to point out. This is purely my opinion and others may say it's not a problem.

First of all, I can't get a grasp of where Kagami got his weapons. You mentioned he was close, but did he run back to where he stored his weapons? Or were they hidden behind the wall he was hiding behind? You left out some details regarding movement and location that makes some portions a bit confusing.

Second,the fight scenes are a bit choppy and reads like a pokemon battle. During the fight, you basically listed what was happening instead of giving a description, it also gave the impression of each persob taking turns performing an action. Unless that is what you are trying to go for, perhaps consider making it more fluid. A fight is a seamless sequence of actions and reactions. Maybe try and combine two actions into the same sentence, actions in a fight are rarely separate. Also some actions can be inferred. For example when Kagami used his spear to hit the bandit, instead of saying "He stabs the bandit with his lance, which is stopped by the bandit’s round shield. The bandit is pushed back, but he calmly swings his mace to Kagami’s face." Perhaps do something like "Kagami thrust at the bandit, the tip glancing off the bandit's raised shield. As the bandit stumbled, he planted his foot and retaliated, swinging his mace up towards Kagami's face. Kagami deflected the blow off his shield and was forced back by the momentum of the blow." The bandit raising his shield to block was implied by the lance hitting a shield. Doing this also combines the strike and block in the same instant instead of two separate moments. The same criticism also applies to the rest of the exposition, although it is less of a problem there. I also fall prey to this mistake, so you aren't alone in having to improve this.

Finally, this is a small problem and it probably won't bother most people. But during the scene where Kagami gets shot, the reaction timeframe is a bit off. Kagami saw the bandit pull back the bowstring, but he barely dodged the arrow. It seems like the arrow teleported or something. Unless it is actually a teleporting arrow, it might be better to change it to seeing the bandit let loose an arrow instead of drawing the bow. That gives a good timeframe to "barely dodge" because any self respecting warrior would start moving as soon as he or she notices a nocked arrow and thus it wouldn't be "barely dodged".

So all in all, the story seems like a list of actions, events, and descriptions, instead of a fluid sequence. There are some location and movement details missing, and perhaps consider the timing of some of the action-reaction pairings then change the writing accordingly.