This is a straightforward ascent of Purple Mountain and three summits north of it, (Tomies, Purple NE and Shehy). From the carpark at Kate Kearney's head south to the unpaved road shown (the rightmost of two adjacent roads). The ascent goes north following a spur off Tomies. There is a choice of ascending to the right (west) or left (east) of a deer fence. Go right.
The fast but arduous ascent goes on a track through high heather until about the 500m mark, whereupon the gradient eases off and the vegetation becomes easier.
For myself, the ascent of Shehy was the last, currently the 269th, of my round of the Vandeleur-Lynams.