The elevation of my house is covered with roof shingles. There are no problems with the exterior wall or the shingles, except aesthetics.
I want to cover the shingles with board and batten on furring strips. Can I do this directly on top of the shingles or should I remove the shingles first?

Putting board and batten over existing shingles sounds like a moisture problem waiting to happen. Board and batten is not water tight and would allow moisture to rot away at the shingles behind. Best bet would be to remove shingles and make sure you have typar or some water shield on sheathing before installing new siding. Not only the moisture problem, but with the singles still in place, the board and batten will probably stick out past your door and window trim, looking pretty funny, hope I could help

I agree, I wouldn't put it over the existing shingles. Tear it all off, put a good weather barrier (Tyvek) on, flash out all of the windows and doors, then put your board and batten siding on.