Bosses are the main baddies in the game.  You must kill them to further the game.  Most of them will give you one of the tokens required to restore one of the Pillars.  So... yeah... you gotta beat them.

Nupraptor the Mentalist
LocationNupraptor's Retreat
Starts by emitting a row of energy balls in a horizontal line across the screen.  You can see that they are mostly green with a few purple.  There are also a few spikes placed here and there.  Make your way through the purple energy balls, past the spikes to hit Nupraptor.  After doing so, he teleports to the other side of the screen and does this again.  Rinse and repeat a few times.  He will then teleport to the center of the screen.  Hit him once more and he should go down.
Malek the Damned Warrior
LocationMalek's Bastion
He swings a long pole arm, but is somewhat slow.  Hit him a few times (and without being hit back in the process, cus it's gonna hurt) and he'll fall to the ground.  Upon getting up, he will shoot energy beams at you.  This is where you try to outrun them until they dissipate or you use Repel.  After doing this about 4 times.  He'll go up the to top of the room and release a large energy wave that you can't stop or get past.  Now, you have to flee towards the SE corner of the room and exit through the teleporter pad.
Bane the Druid
LocationDark Eden
Bane is fought along side Dejoule in this battle.  Bane's ability is to turn land into water, making it more difficult for you to navigate through without taking damage.  Other than that, he is pretty much pathetic.  Hit him a few times, and he'll go down and you'll get is head piece thingy.  You also have to dodge energy bolts being fired from Dejoule in the process of killing him.
Dejoule the Energist
LocationDark Eden
Try to take her out only after killing Bane to keep him from turning ground into water.  She shoots out energy bolts that somewhat home in on you.  At the same time, she is also surrounded by a rotating energy field.  Just use 'Repel' and stand up near the water and shoot out your Energy Bolt spell or Flay or whatever else kind of projectile weapon you have to try and hit her a few times.  And that's pretty much it.  She doesn't move around or do any other attack.
Azimuth the Planer
LocationAvernus' Cathedral
She starts by summoning 2 demons to sick after you, while at the same time she throws homing Energy Bolts at you.  When you kill the 2 demons, she will just summon 2 more, so ignore them for now.  Start by using Repel to deflect there attacks and her Energy Bolt spells.  Now, equip the Soul Reaver and with a strong, fully magic-powered swing, you should be able to take her out in one blow.  If you'd rather not use the Soul Reaver to save up on magic for a recast of Repel, the Flame Sword will work just as well; just takes an extra couple of swings.  If you are too slow in hitting her, she will teleport to the other side of the screen so you have to be quick about it.
Elzevir the Dollmaker
LocationDollmaker's Mansion
Pretty much almost the same fighting style as Azimuth, but instead of demons and energy bolts, it's teddy bears and arrows; he also doesn't teleport if you're too slow in hitting him.  The same strategy can be applied here for taking him down as it did for Azimuth.
William the Just
LocationWilliam the Just's Stronghold
He is a pretty tough boss.  He fights along side several guards and wields a Soul Reaver (nyah?!).  Use Repel and equip the Flame Sword and just start hacking away.  Remember to keep recasting Repel when needed so you don't re-die a most horrible and probably uncomfortable death (you DO have several Heart of Darkness objects on you, right?).  You can risk it and use the Soul Reaver, but that will drain your magic and leave you vulnerable to their attacks when your Repel wears off.  After beating him, some more guards will attack you.
Mortanius the Necromancer
LocationThe Pillars at the end of the game
He's not too difficult.  He will summon some lesser undead, such as skeletons & ghouls, to try and smite you down.  Just use Repel, equip the Flame Sword (or Reaver), and start smacking skulls.  After a few hits, he will teleport to another spot.  Find him and continue the beatdown.  He should go down with little to no trouble... until you meet:
Dark Entity
LocationThe Pillars at the end of the game
The Final Boss in the game.  This is where Mortanius merges with the Dark Entity to engage you in battle.  He attacks you by disappearing beneath the ground, then reappears and tries to crush you with his body.  Simply use (yet again) Repel spell and Flame Sword (or Soul Reaver if you want; 2 fully charged swings should do the trick).  When you use Repel and he comes out the ground, you won't take damage.. so just kill away.  He'll be dead after a while, and you can view the ending of the game.