All I can say is that the game is quite beatable with quite a number of different combinations, including a team made up of same unit type or of all 8 different units (exception would be one or two challenges that have a boss immune to physical attacks). For instance, instead of having a healer, having 4 Psy Fighters specializing in 4 different elemental attacks with Vengeance will make 4 quite all-round self-supporting units. Then again, having a mostly Shadowling/Spriggat team might have its disadvanatge of having restriced elemental attacks against enemies with resistance to them, so some maps will be much harder than others (same goes for mostly-ghost maps agains melee teammates).
Another point to make is that no matter what, try not to lose any units: it's not worth losing one after training it hard, then buying a new one- the gold investment is too high, especially towards the latter stages of the torunament.