Yes, you have to make a check for each spell. When there are a very large number of spells active, your DM might choose to let you take the average -- for example if you have a 35% chance to dispel a spell, your DM might rule that you dispel 35% of the 390 spells, so 136 of the spells would be dispelled. Your next attempt could dispel 35% of the remaining spells, et cetera.
A good way to generate the massive number of dispel checks you need would be to cast dispelling screen, which is a fourth-level wizard spell which casts targeted dispel on anyone who walks through it. Your friend could walk back and forth through it and get rid of the effects pretty quickly.
I'll note that the standard contingency spell is self-only, and only one can exist at a time, so it sounds like your DM has a houseruled spell running.
I'll also suggest that it would be a good idea to find out what all those contingent spells do before you start messing with them. What if they're protective: "if the target drops to negative hit points, cast cure serious wounds on her"? What if some of them are meant to prevent you from dispelling the others? "If someone casts dispel magic on this target, respond by casting fireball".