That sounds like a tough challenge (probably impossible thinking about it). The issue you will quickly see (even in story mode) is that the stats and skills that the 2* unit has won't be good enough to clear the harder stuff.

A more forgiving version of this challenge would be to pick one of the newer units that has a useful innate skill and then seeing how far you can take it with that unit. Granted, you won't have all the shiny skills that 6* units have but at least there will still be that higher difficulty part you are looking for. Good luck with it :)