Red Orbs are the equivalent of currency in other games. All of Dante's moves and some of your Health and Devil Trigger Upgrades (as well as some items) are bought from the shop between missions and from the golden Divinity Statues inside missions. You will be awarded more orbs if you kill enemies with high style or for completing missions with a high rank, which gets very technical and often boils down to taking no damage at all. Because of this, you will be doing one ethical grind early on and skipping most of the intended progression.

Refer to  Redemption for the early farming strategy.