I hiked this with Bill K7WXW and my wife as part of a two summit hike. I don't have much to add that Bill didn't say. There is a 1/3 mile section at the start that is a marshy, overgrown slog on a steep hillside. Bill got stuck in the muck a couple of times. I didn't know if I should help him or use him as a human bridge over the bog. Mosquitos in that section were horrendous. The rest of the hike was steep and trail finding was challenging. It did have wild lilies and other flowers that gave the hike some redeeming value. View from the top was OK, but it is in burnt trees so not exactly a lovely picnic spot.
I will probably hike Battle Ax again but not sure Beachie is worth the 4 points. If you want to do both, start with Mt Beachie so you can enjoy lunch on Battle Ax. There are references to a trail on the east ridge that goes to East Mt Beachie and then the summit. Bill and I studied the ridge and did't see an obivious route. It is worth a try, but make sure to review info on climbing sites.
The first picture is me setting up an 40m EFHW and Bill on 2m. The second picture is looking east from the summit. The last picture is us entering the 1/3 mile slog on the way down.
Here are the GPS tracks for Mt Beachie from Elk lake and Battle Ax:
http://www.pnwsota.org/content/wx7or-beachie-gps-track
http://www.pnwsota.org/content/wx7or-battle-ax-beachie-gps-track
Jeff
WX7OR