To earn high chaos, you need to kill your targets, their guards, non-soldier/guard enemies, and civilians. There is no set number of people you need to kill each mission to earn high chaos, you simply need to kill anyone you can see and you will have no problem earning high chaos. This is by far the easier of the two required playthroughs, but just in case you need some help I will list some general tips below.
You get one free rune, I highly suggest you use it to unlock 'summon assassin'. With summon assassin, anytime you get in a fight you will be able to (like the name says) summon an assassin. The assassin will remain with you until he’s killed all enemies in your vicinity, or dies trying. Having some backup can make fights really easy, especially in the last mission.
Don’t buy any crossbow bolts until the final mission. In the first and second missions, you can find pistols and pistol ammo very easily. Not buying crossbow bolts also saves you money for better upgrades later in the game.
If you want to kill stealthily so you don’t have to get into open fights, then purchase the shadowkill power. Combining this ability (which turns stealth killed enemies to ash) with blink can be an awesome lethal-stealth combo.