I am not going to describe basic mountain hiking safety in this post. You must make sure you understand basic mountain hiking safety before trying to hike Beidawushan, or any other high mountain.
The new trailhead for the national trail is at around 1100 meters above sea level, Cedar Valley Lodge is about 2100 meters above sea level, and the summit is 3090 meters above sea level. Thus, if you follow a standard 3-day/2-night itinerary, the elevations look like this:
Day 1: ~7 km distance, +1000m altitude
Day 2: ~5 km distance, +1000m altitude, then in reverse ~5 km distance, -1000m altitude (note that there is a lot of up-and-down on the ridge itself)
Day 3: ~7 km distance, -1000m altitude
As you can see, Day 2 can be pretty steep.
You do not need special climbing equipment for the national trail, but many sections require ropes (already in place), including a few landslides, lots of rocky scrambles, and some “exciting” bits on the ridge itself where you can fall to your death. If you have a thing about heights or exposed narrow ridge trails, think carefully before trying this hike. This is all much more dangerous in wet weather than dry weather.
Due to the abundance of moisture and life, to quote the Pingdong Forestry Bureau, “Leeches may kiss your feet”. Somehow, my feet have never been ‘kissed’ in places which are notorious for leeches (Jin Shui Ying Trail, Walami Trail, Wulai, etc.) yet they get ‘kissed’ in places like Yangmingshan National Park and Alishan.
Routes other than the national trail will probably need additional equipment, so you will need to ask someone with deep knowledge of the area to know what to bring. Someone I know who hiked Beidawushan from the Taidong direction said that he needed a machete.
You can check trail conditions on the national trail at this website if you understand Chinese. The trail is often closed due to typhoon damage.
Speaking of typhoon damage, never go there when a typhoon is coming or right after a typhoon. Even when there is no typhoon, high mountain weather in Taiwan can be extreme and change quickly. Do check the weather reports for Taiwu township, but understand that the weather at mid-elevations (which is what is forecast) may not reflect the weather at high elevations.
Beidawushan is in southern Taiwan, so the rainy season is May-October, and the dry season is November-April. Generally, dry weather is safer than wet weather. June-September is also the typhoon season, though typhoons can also happen in May and October.
Like other high mountains in Taiwan, summer rain tends to happen in the afternoon, so if you hike in the summer, plan to do most of your hiking in the morning.
It rarely snows in Beidawushan (i.e. it does not happen every year) but snow is possible in winter, and can mess up your hike if you are not prepared. Generally, winter weather in the high mountains can be fierce even without snow.
The safest times to hike are November-early December, and March-April. May is the best time to see rhododendron flowers.