Keeper Is Dead

Finish the game on any difficulty level.
The boss fight against the Keeper comes in three stages:

Stage One: it's you vs. the Keeper; he will be protected by magic armour - when the armour is red, you need to use an ice spell (Circle Button, Triangle Button); when the armour is blue, you need to use a fire spell (Circle Button, Square Button); two casts of the regular forms of those spells will destroy his armour, and once it's down hit him with a Heavy Strike (which does the most damage to him by far). His attacks in this stage will consist of a string of fireballs (fly diagonally towards him - X Button + X Button to fly - to avoid the fireballs), a freezing shockwave, and an area of effect ground pound.

On normal difficulty this stage isn't too bad - keep your health up and try to be rapid with your attacks and he'll go down pretty quickly. Hard difficulty is a whole other beast, however: a direct hit from his fireball attack will kill you; an indirect hit will drain almost all of a full life bar. You need to be quick but strategic on hard - if, for example, you're at half health and can't heal yourself any further, don't rush him and risk being wiped out by a fireball; just be patient and wait for your health to recover. The fight is basically the same, you just have to be a bit more aware of your health and his attacks. I also recommend the following equipment (all of which you should have by the end of your Hard playthrough):

Swords of Pain: Health buff, and Rage doesn't completely reset after receiving health points
Dragon Claw Rifle: Increase the range of Heavy Strike, more damage against armoured enemies
Amulet of Strong Health Increase total health, increased resistance to ranged damage
Mysterious Ring: Increase speed

The health buffs stack, and the speed increase should help considerably with dodging the fireballs (which have a ridiculously wide blowback effect).

Stage 2: Michelle and Zero run around destroying some machinery that prevents the portal from opening, and it's your job to keep the Keeper busy while they're doing it; luckily, there are waves of monsters attacking him as well, so this is the easiest stage of the fight; if you're not worried about how long it takes, just keep your distance and shoot him with your rifle; if you want things to go faster, occasionally get close to him with enough magic to cast a spell and destroy his shield; however you play this part, Michelle and Zero will destroy four things and the portal will activate.

Stage 3: You're back where you began, and the Keeper has tried to follow you through the portal but is stuck.

During this stage you will have to defeat waves of monsters and avoid a spell cast repeatedly by the Keeper that has a truly ridiculous area of effect. Defeating each wave of monsters allows you to attack the Keeper directly for a few seconds, then he knocks you back and you'll have to defeat another wave of monsters to get another crack at him.

There's not much to say about this stage: Michelle and Zero cannot die, so if you're out of health don't think twice about retreating and buying yourself some time. As mentioned, the Keeper's spell covers a ridiculous amount space - don't dawdle in it, as it does a ton of damage.

The only thing that really needs to be pointed out here is that you should always let Michelle and Zero get to the Keeper first: he will always do a ground pound when the first person runs up to him, so let your cohorts run up there and get smacked, then follow afterwards.

Clear waves of enemies, then attack the Keeper, and cast Heavy Strike when you get the chance.