Position the battery holder in between the folds of your bow tie, and secure at least two of the corner mounting holes to the fabric with a few stitches of plain thread. This will prevent the component from sliding around while you're sewing other parts of the circuit.
Double check your needle fits through the holes on the battery board-- they are on the smaller size. Thread your needle with conductive thread and connect it up to either the SW or Gnd pad on the board and get to stitching towards your sequins according to the circuit diagram and your desired layout.
To bring the conductive thread to the outer pads on the sequins, use shallow stitches that just barely catch the surface of the fabric, so they don't show through on the front side.
Seal your knots with clear nail polish, being careful not to get any on the pads of the circuit board. LESS IS MORE.
Pull the thread tails taut while the nail polish dries, and double check that it's "glued" in position before cutting the thread tail short. Conductive thread is very springy and your knots will spring open if you skip this step!