I am Vengeance (10 Points)
Achievement Reward: Banner Accent (Demon Hunter's Crest)
Complete Act IV with a Demon Hunter on Normal Difficulty
Dreamless Sleep (10 Points)
Complete Act IV with a Demon Hunter on Nightmare Difficulty
Hell Hath No Fury (10 Points)
Complete Act IV with a Demon Hunter on Hell Difficulty
Grandmaster Hunter (10 Points)
Achievement Rewards: Banner Sigil (Hunter's Rune)
Complete Act IV with a Demon Hunter on Inferno Difficulty
Disciples of the Night (10 Points)
Reach Level 60 with 2 Demon Hunters
Death Dealer (10 Points)
Equip a Cloak and a Hand Crossbow at the same time.
These items drop from monsters so should be easy to get, but if you are having problem finding a specific item you can buy from merchant, or from Auction House.
Olympian (10 Pts)
Use Vault 6 times in 10 seconds
Easiest to get after Lvl 33 when you have access to the Tumble Rune. Preparation (Level 13 skill that restores discipline) also helps.
Death Trap (10 Points)
Achievement Rewards: Banner Accent (Arrows)
Kill 15 monsters in 5 seconds using Spike Traps
The Level 55 Scatter Rune is a good one to use for this if you are having difficulties
Longshot (10 Pts)
Kill 100 monsters from 45 yards away
Bleed, you Filth! (10 Pts)
Damage 20 enemies with one Fan of Knives
Take advantage of the Level 38 Rune "Hall of Knives" to help you unlock this achievement.
But You Can't Hide (10 Pts)
Kill 100 enemies that are running away
Imps have a tendency to run away so they might be good targets, or use a skill that causes fear on the enemies
Hunter or Hunted (10 Pts)
Kill 100,000 demons
This will take a long time and will probably require a bit of grinding demons...
Right Where I Want You (10 Points)
Keep a boss snared using Caltrops for 40 consecutive seconds
Azmodan is a good one to try this on
The Madness Contained (10 Points)
Spend 150 Hatred and 50 Discipline in 6 seconds
Try Shadow Power, Smoke Screen, and Preparation.