When to go Taiwan (when to travel):The best months are May, June and October, in which the temperatures are warm (but not muggy) and the rain is moderate (in Taiwan it rains a lot).
April is a month in which anything can happen ... normally it doesn't rain much but the water is usually fresh for activities in rivers and waterfalls ... but for the rest of the trekkings, activities and visits it is an appropriate month.
July, August and September are typhoon (hurricane) season, so it is best to avoid them. Taiwan is usually hit by 3-5 typhoons during these months. What has to be said is that it is a very safe country, and they take many precautions so that these natural phenomena do not have catastrophic consequences. So we do not close the possibility of going to the beginning of July or the end of September, when the probability of typhoons is not so high, but the weather is good for bathing in rivers and waterfalls.
It is better to also avoid the winter months (November to March), since it is cold and rains a lot in the north and center of the island. You will not be able to enjoy the rivers and waterfalls, and the trekkings will be really cold and wet.
You also have to be careful with the Lunar New Year (Chinese New Year), since it is the most important holiday period of the year, everything is full and you have to book well in advance. The date changes but it is usually around February.