Park at Lettergesh Beach car park. The rocky summit dome of Benchoona is already visible off to the left. Walk back up to the road and turn left. 150m further on is a little unsignposted lane going up to the right. This GPS track begins and ends at the entrance to the lane.
The lane goes past several houses then comes to a gate with a "Keep Gate Closed" sign. Go through it, and the lane continues up quite steeply to a water treatment plant on the hillside. (This is clearly visible from the road, so if the route is unclear, look for the plant and try and trace the lane down from it.)
Past the water treatment plant, the lane turns into a grass and gravel track. Soon it comes to a second gate, this one bearing a "No dogs allowed" sign. Go through the gate, unless you have or are a dog. The track continues with a stream with very steep banks on the right. After just a minute or so, the track crosses the stream via a sturdy concrete bridge. Don't cross the bridge, but head off the track and to the left to Benchoona,
whose rocky dome (not really a dome, but it looks like one from this side) is still just visible over the nearer slopes.
The second ("No Dogs Allowed") gate, with the stream running alongside it on the other side of the fence. Benchoona is off to the left. Altnagaighera is just visible on the skyline:
The route from here to the top is a matter of preference. My route could probably be bettered, but it got me there without much drama, just a lot of zig-zagging on the rocky high slopes (no scrambling needed).
It's all easy walking from Benchoona onwards, with no substantial ascents. The walk along the pleasantly narrow ridge to the minor top referred to variously as Altnagaighera/Binn Fraoigh/Garraun SW is well worth doing, and the descent from there is easy, though there are a few rocky outcrops to be avoided further down.
The ruins of a structure of some sort on the slopes of Bechoona. The little gorge running through the bog is also visible in the middleground:
On the descent from Altnagaighera and in the boggy plains below it's best to stay right of the stream that starts on the mountainside and leads all the way back to the bridge that you didn't cross on the way up. This stream has formed a little gorge through the bog which is a nice feature. Anyway, finally cross the aforementioned bridge and back down the lane past the water treatment plant and there you are.
The journey time that appeared when I created and uploaded the GPx is not accurate and not the same time as appeared when I synced my watch with Garmin Express. It took 2 hours and 6 minutes, not 1 hour 40. (And distance was 9.33km, rather than 8.8km.) This time is for a solo walk with only a few quick photos stops and including a bit of running on the descent.