For such a small hill Bouleevin has a lot to attract it. I really loved the scrambling opportunities and the limestone pavement in the area is spectacular.
I started where Sandman suggested and followed his route past to open countryside but, instead of heading directly for the summit, I headed NE to M34272 03258 C and from here headed south along the ridge. There were a couple of ups and downs on the way with some nice minor bits of scrambling, all avoidable. It's an easy route with a lot of grass underfoot once yiou get past the limestone.
From the summit I headed to Turloughmore Mountain but first I descended maybe 30 metres to the west so I could enjoy a walk across the numerous stretches of clints and grikes in the area. Eventually these petered out and I started climbing again to reach the summit of Turloughmore...great views of Knockanes and Mullaghmore form here. From here I had intended to drop to R33260 98418 D and to walk back the road to my car but, having spent too much time dawdling, I decided to back track and ended up accidentally hitting the road at more or less the same place as James Sheerin. The descent was easy enough but you need to keep a keen lookout for gaps in the scrub as you're moving down. A highly recommended circuit which took me a very leisurely 3.5 hours. Linkback: https://mountainviews.ie/summit/1260/comment/22520/