Unlock the following Avatar Awards by performing the corresponding tasks:

AVATAR AWARD - HOW TO UNLOCK
Death Knight Helm - Collect 20 Treasures.
Pocket Shaman - Defeat a Primitive Shaman.

The Unicorn Armor is obtained by unlocking the Special Delivery achievement (carry the present out of Palace of Death on at least the Hard difficulty setting). This is best done by dropping the present at the start of each room and, after putting some distance between you and the box, killing all enemies to advance. Be wary of ranged attacks (auto aim) and explosive/poison barrels.

Drop the present at the start of each room. After that, make some distance between you and the box, then kill all enemies to advance.

"Vengeance Map Pack" achievements
ACHIEVEMENT - HOW TO UNLOCK
Tough as Nails (15 points) - Survive Fistful of Coins wave 7 on at least normal difficulty.
Way of the Ninja (15 points) - Complete Dead Among Us.
Burning Down the House (20 points) - Complete Inferno.

ACHIEVEMENT - HOW TO UNLOCK
I Have The Power! (10 points) - Unleash your Ultimate attack.
Three-peat (10 points) - Earn a gold medal on Fall of Byzan with each character class.
Big Bang Theory (10 points) - Kill 25 enemies with explosive barrels in a single level.
I'm Not Dead Yet! (20 points) - Revive yourself while playing alone.
Maxed Out (20 points) - Max out any character stat.
Special Delivery (20 points) - Carry the present out of Palace of Death on at least hard difficulty.
Soul Hoarder (20 points) - Find and collect all 33 Soul Anchors.
Rampage (10 points) - Achieve a score multiplier of 8X on at least normal difficulty.
Horny Devil (20 points) - Defeat Gashadokuro, the Death Knight.
Bring Out Your Dead! (20 points) - Complete Requiem.
Soul Survivor (20 points) - Defeat the Soul Siren.
Go for the Gold (20 points) - Earn a gold medal or better on every Main Campaign level on at least normal difficulty