After reaching Demon Ruins from Queelag Domain , light on the bonfire next to the entrance. 
There are two ways leading from this place. First you have to go to the right over the bridge to defeat demon Ceaseless Discharge.
Once you kill the demon, run down the slope, ignoring creatures with eggs on their backs.
When you get down, you'll be able to go in two ways again. In front of you, in a distance, you'll see small versions of Taurus Demon.  To the right, along the slope, you can see a path to another part of this location. If you go there, you'll find small version of Capra Demon and two more bosses. 
First clear the left side of the location - lure out mini tauruses one by one with your bow.  During the fight just dodge their slow attack (an alternative method is to equip a strong shield and armor - Stone Armor). A spear with lightning effect will do well. 
Once you kill Tauruses, explore the location in search for items. The most interesting is Chaos Flame Ember located in lava at the end of this path. In order to take it out of the lava you may consider dying - but this is worth it, because it will allow you to create best fire weapons. If you have problems with collecting this item, ignore it for now - soon you'll get a ring protecting from lava.
Go to the opposite direction, towards a bridge, along rocks.  You'll find there a descend down with pillars.  A bit further small Capra Demon is lurking, accompanied by some "brothers". Lure out the best to the open area.
During the fight with small Capra Demon, you have to jump aside when he wants to make an attack from above his head (when he crosses his blades) and block other weaker blows.
Go down the slope behind the first Capra Demon but be very careful.  In the ruins below you'll see the entire group of these enemies. Lure them out one by one and kill them. 
If you character is strong, you can fight with Capra Demons on a slope. But it is safer to lure them on the open area.  Before you enter the ruins, lure out one more Capra, standing on the lower level. 
Run down the stairs.  At the bottom watch out for statues - some of them will come to life.  A fight with them is easy, because these opponents are very slow. When the enemy starts spiting fire, go around him and attack from behind.
Run towards the wall and turn left - you'll see a giant centipede on a horizon.  Kill the monster.