It's hardly the most remote trail in the Carpathians, but the popular ascent to Ukraine's highest peak is relatively easy to achieve. On a clear day, the expansive views from Mt Hoverla are also breathtaking. Initially, the trail follows the Yaremche–Vorokhta–Zaroslyak road, so how much of the way you want to hike and how much you want to cover by marshrutka (which go as far as Vorokhta) or taxi is up to you.
About 7km south of Vorokhta you will need to take the right fork in the road, heading west. En route, you will cross the CNNP boundary and pay the entrance fee. From Zaroslyak (20km from Vorokhta) it's about 3.5km to the summit of Mt Hoverla, which is marked with a big iron cross and a huge Ukrainian national flag (which has now been joined by an equally large EU flag).
Along the Chornohora Ridge
The southern Chornohora peak of Mt Pip Ivan Chornohirsky (2028m) is well known for the abandoned astronomical observatory atop it. The Poles completed this observatory just before WWII, and anything of value has been looted, but the place stills retains atmosphere.
One of the easiest routes to Pip Ivan is along the crest of the Chornohora ridge from Mt Hoverla via Lake Nesamovyte. It's hard to get lost this way, as your views are unimpeded, and the route follows the former interwar border between Poland and Czechoslovakia, passing the old boundary markers. At more than 40km return, the hike will take at least three days.
Other routes to Pip Ivan include coming from the village of Verkhovyna via Dzembronya and over Mt Smotrych (requiring at least one night's camping). Alternatively, you can approach the mountain from Rakhiv.