When you complete the following tasks you will be rewarded with the corresponding avatar.
Unlock Freaky Slippers (Male and Female):
Complete the 'First Hurdle' achievement.
Unlock Level 1 Agent Suit (Male and Female):
Complete the 'Light Bringer' achievement.
Unlock Official Agency Hoodie (Male and Female):
Complete the 'Jack of all Trades' achievement.
Unlock Ruffian Hat:
Complete the 'Hope Spring Savior' achievement.
Unlock Orb Shirt (Male and Female):
'First Blood' achievement detected from Crackdown.