Kill Hermes and acquire his Boots

Pull over while the police are in 'pull over' mode, then drive away during the ticketing cutscene.

Complete one of the missions you receive in the mission log.

Complete The Green Sabre.

Purchase any house.

Use a Pay 'n' Spray with wanted level.

Melee 5 enemies in a row.

Kill Helios

Cover Kratos in 500 buckets of blood by killing the enemies

Upgrade any weapon to the next level

Acquire the Bow of Apollo

Rescue Woods.