This top is normally done in conjunction with others on the Glenbeigh Horseshoe, and it is almost impossible to access in isolation. The simples approach is via Drung Hill.
Heading west from Glenbeigh turn off the N70 V630 890 A and follow the narrow road for about 1km to point V622 888 B, where there is room to park a couple of cars on the roadside.
Walk west for 100 meters and follow the waymarked way sign up a track left at V61p 887.
Continue through several gates until you reach V607 887 C. Cross the fence and head straight up Drung Hill, which has steep slopes, but the terrain is naturally 'stepped', which helps the ascent. When you reach the summit of Drung Hill, head directly SW for 1km over solid, grassy terrain, and you will reach Beenmore in about 20 minutes, the summit being marked by a cairn. Linkback: https://mountainviews.ie/summit/173/comment/4933/

Dark cairn jagged

against mist of Kells

Kerry coast and

sun off sea. Linkback: https://mountainviews.ie/summit/173/comment/1911/

I climbed Beenmore via the summit ridge from Drung Hill which took around 25 minutes. There is a cairn at the summit which had a grid ref. on my GPS of V59641 86790 D. There are stunning views(on a clear day!) across to the Dingle peninsula and the Slieve Mish mountains. I had intended to walk across to Been Hill but unfortunately ran out of daylight. As I mentioned in my Drung Hill comments, I walked for 6 hours on a beautiful frosty day in January and only met one other person - a Kerry farmer! That is the beauty of hill walking in Kerry! Linkback: https://mountainviews.ie/summit/173/comment/4391/

Martin Critchley (Track 2577) says of the extended Glenbeigh Horseshoe filmed by Sharron Schwartz and he:
This route takes in not just the classic Glenbeigh horseshoe but includes most of the extra summits to the east. The route starts at Glenbeigh and takes a minor road heading south for 1km before turning left onto the Kerry Way which is followed to a col. Turning right at the col leads to the start of the traverse and the first summit, Coolroe. If time permits it is also possible to turn left at the col to make a detour out and back to Seefin. In addition, again if time permits, it also possible to traverse out and back to Colly. But including Seefin and Colly on this traverse would make it hard to complete these and the whole traverse in a day (we did Colly alone the next day). The highlight is probably the spectacular knife ridge traverse out and back to Keamconneragh (a traverse perhaps to avoid on a wet or misty day where a slip might have serious consequences). The downside to the route are the numerous peat hags in many of the cols (and some of the summits) which make for slow progress.
Highly recommended film by two of Ireland's top mountain moviemakers.
https://www.youtube.com/watch?v=dVBxp44ziEs Linkback: https://mountainviews.ie/summit/173/comment/17719/