Best thing I can think of for you.
4ea. SSP-1 clips
2ea. - 2' DWFC (7/8" drywall furring channel)
2lf. 1/4" SSP Mat w/psa
attach clips and channel to wall, attach 1/4" foam to back of board, attach board to channel (screws cannot touch wall or clips). Attach dart board to back board.
you can also attach a layer of foam to the back of the dart board to reduce it more.