This stage is really simple, all you have to do is jump around and kill all the Hell Prides and Hell Lusts (Hell Wraths on higher difficulties) that lurk in your shop. More will continue to spawn inside your shop and attack you, simply kill them as they come at you. This mission and the next mission serve as a trial-by-fire tutorial. Experiment with the controls and continue fighting the demons. Accessing the "actions" sub menu in the pause menu will display all of the attacks currently at your disposal.
With Vergil, it's the same still, just evade and attack all the demons until they are all defeated.
An easy way to gather red orbs is to play this mission multiple times early on since this mission can be done quickly and usually gives a high rank,you can amass many red orbs before continuing on in the game.