Successfully complete the game on any difficulty setting to unlock Blade and Classic Ghost Rider. Successfully complete the game on the Normal difficulty setting to unlock Inifinite Link, Inifinite Spirit, Invincibility, First Mortal Blow, and Turbo Mode. Successfully complete Story and Challenge mode on the Punishing difficulty setting to unlock Ghost Rider 2099.
Get all skulls in Story and Challenge mode to unlock Vengeance.
Buy the first upgrade for the Hell-Cycle. When fighting Vengeance, make sure that you have the course memorized. During the fight, rapidly press Circle to fire your upgraded homing shots in a constant stream. If done correctly, his health will decrease quickly and you will get the time challenge skull.