You can access this trail from either the Beachie Saddle from the Battle Axe Tie
trail or from about 1.8 miles from the south end of Bagby Trail #544
. This makes a good loop. It's best to park on NF-4697 at the top of NF-390 to Elk Lake. There is room for only a few cars here along the side of the road.
From Beachie Saddle start climbing north on the rocky trail. The trail is steep and doesn't let up until the summit. It is also rocky and open. This means that you'll have fabulous views of Mount Jefferson nearly the whole way up, and views to Three Finger Jack, Mount Washington, and the Sisters from about half way up. It also means you'll be in the sun the whole way up so bring plenty of water and sunscreen.
The summit of Battle Ax is long and thin resulting in plenty of space to hangout (and even some camping spots). There are the remains of the foundation of an old fire tower near the true summit. You'll be treated to 360 degree views of everything from the coastal range, to Saint Helens, Rainier, Adams, Hood, Jefferson of course, the Sisters, and even Diamond Peak far to the south.
The trail descends the north face of the mountain on some pretty steep switchbacks that are less rocky and more wooded. You'll still be treated to great views of Jefferson over a few scree fields. It will straighten out for about a mile and then meet the Bagby Trail #544
which you can take back to NF-4697.