Don't fight him straight up. Lure him back into the area with all the catapult / trebuchets. One of the trebuchets is positioned in the middle of the walkway, allowing for full movement around all sides of it (I believe it's the third from the doorway leading to the red eye knight).

Take position on the other side of it and make sure to stay on the side opposite the red eye knight as he tries to move around it to get to you. Be careful not to get too close on the other side as he does have a lunge move and can still hit you, even if the trebuchet is directly between the two of you.

From here you have two options:

a) Wait him out. He will eventually tire of chasing you around the trebuchet and will leave to go back to his original spot. Once he begins to walk away, you can run up behind him and land a critical hit. Rinse, repeat until dead. Takes 15-20 minutes, but works.

b) Lure him into making one of those spear lunges by getting close to him on the opposite side of the trebuchet. When he starts to charge, back up to where he can't hit you and then pop him with magic / firebomb / arrow. The timing is important because when he lunges, his shield is down, allowing for much greater damage. Start to cast / throw / shoot when you hear his charge sound. This is considerably quicker, once you figure out how to lure him into a spear lunge.

Wait until you level up enough to have magic spells. You'll have to beat Phalanx in 1-1 before you can start acquiring magic spells. The first catalyst in the game is a wooden one that is on top of one of the towers in 1-2 along the bridge immediately after Phalanx. You will also want to equip the Thief's Ring.

Once you have the catalyst, go learn either basic offensive spell. The Soul Arrow is probably the best choice because of world 2-1. I ground enough to get the Flame spell as well.

Once you have one of those spells, walk up to the spot where the red eye knight stands, but do so very slowly. Try to lock onto him. If you can't very slowly take another step forward until you can. Then shoot one of the spells at him. He'll take a pile of damage and start chasing you. Turn around and sprint out to the spot where the trebuchets are. If you listen carefully, you'll hear the knights footsteps slow as he gives up and turns around to walk back to his spot. As soon as he stops chasing, you can turn around and walk up behind him again. As soon as you can lock on, shoot him again. Only takes four hits like this to kill him. Be careful how quickly you return for later shots, though, because if you don't let him walk far enough back and "think" you're completely gone, he'll heal himself up and you'll run out of MP before you kill him.

Also, only cast one spell at a time! As soon as the first one hits for big damage, he turns and raises his shield, which will effectively deflect any subsequent spells until he drops his guard again.

The first time I played through I stood outside the room with the "named guy" trapped on the ledge (the guy with the ornate shield that you help/save in 1-1, 1-2, 1-3 etc). I ended up sniping him with magic thinking he was a sub-boss or something. I killed him and picked up the keys off his corpse. No reason to go beyond the locked door at a low level, but still...