Easy Red Orbs (Mission 7)
~4,300 red orbs in about 20 seconds.
Easy red orbs in Mission 7: The She-Viper in Devil May Cry 4.
For about 4,300 Red Orbs in ~20 seconds: at the start of the mission, destroy the rocks to your left. Enter the tunnel and destroy the rocks. You'll see the big red crystal near the Secret Mission. For the most orbs, start with the Stinger, immediately activate Devil Trigger and quickly mash away. Then pause, choose "Systems" > "Retry Mission". This is the easiest way to farm a lot of orbs quickly.