There are plenty of ways to do it, just use your brain and figure it out yourself. You can take essentially any class there.
High Priest?
Sure, with the HP SQI you've got Colt Bolt, if you have a Doppel weapon that HP can wear you can get a fire endow and whack them to death, priests can heal themselves.
The best class it debatable, but Mavkas are low tier monsters, with the right set of gear any class can fair 'decently.' I leveled my Champ there when it was a Monk using combos, I leveled my Hunter there with Double Strafe, I leveled my Sage there using an autocast build, I leveled my Knight there using pierce, I leveled my SUPER NOVICE there using Firebolt, Assassin using 1HKO Sonic Blow. You could mob on a BS, AD with a Bio (Though you'd end up losing more money than you make, likely), Rogue can do the same thing as a Hunter and Bard (albeit less effectively, but they also have high success steal). A Ninja could using their fire magic, a Gunslinger could probably muster a 1HKO with a Fire Endowed Full Buster if they had a VO. Soul Linker works surprising well there since Esma has such a fast cast and they have Kaahi to keep them healed. Star Gladiator would do fine if you focused on kicks instead of heat.
Doing well on any map in this game just takes a knowledge of what works effectively and where.