Castlevania: Order of Ecclesia

1st off, as with most bosses, teleport is your biggest ally, Closely followed by Ignis Kick, just in this specific fight, that can be fatal. You a lot of Max Shots from far away to take out the knees and arrows. Once on his back, your your Optical Shot / Max Shot combo (in that order) on the head - a lot. When he flinches back after doing enough damage, use your Ignis Kick on his eye. It will be right above you and it will give you temporary invincibility.

Or you can do the glitch that makes him easy to beat. when you on his back go towards the golden part of his tail and stand on it. He will try to do moves as if you were at his rear legs. So you can just keep shooting him, but you need to watch out for his attack where he shoots his tail. When he does that just run closer to his eye and when the tail goes down run back to the golden part.

You have to be on Eligor's back to be able to reduce his HP, as was determined by someone on the forums. However, you don't need to destroy his knees or the crossbows to get up there (but you should still destroy at least one crossbow if you're not up for a greater challenge). There are two ways to get onto his back quickly, both of which employ teleportation. Of course, if you want, you can do it the old-fashioned (read: Shanoa fight) way, too.

The first way is to teleport underneath him. Walk up to his legs, then teleport through them. If you do it right, you won't take any damage. Since you're now underneath him, walk to the left, close to his legs. While he's taking a step to the right, teleport behind him, low to the ground. You should get through his legs without damage (if you teleport while he's standing still, you're much more likely to be hit). Now, just get onto his back, either via high jump or teleport.

The second method is slightly faster, allowing you to get from in front of him to his back without going underneath him. You want to stand near his legs to goad him into stabbing the ground, at which point you should backdash to evade the attack. High jump into the air, and teleport to the right of his head. If you're close enough, you'll be able to teleport through him onto his back without taking damage. If you're a little too far away, you'll take damage. If you're too far away, you won't have enough room to tap the screen to the left of his head, and you'll need to teleport closer to the right side of his head. If you've got quick reflexes, high jump up while he's holding his sword at the ready, then teleport through it and proceed as usual; this allows you to get onto his back right at the start, without waiting the second or so it takes for him to point his sword down.

Whichever method you chose, you're now on his back. Jump to attack his eyeball, using Optical Shot, Max Shot, and regular bullets. Once you're dealt enough damage (around 750 HP), he'll grunt and look back, so retreat until you're over his hind legs. From here, Quadruple Ignis (flame kick) to the right as he's coming, and you'll do a little more damage (if you do it wrong, he might push you off his back when he leans). Just repeat the process until he's down. If you need a breather, stand on the glitch spot. Note that Eligor's eyeball has slightly different weaknesses than his body, such as being weak to slash attacks instead of strike attacks (for the record, the bullets fired by Albus' normal attack are slash-attribute).

I have used the L. eye of god, hurting him while he is leaning backwards doesn't actuly take down hp.