Laurjoyce, I've replied to your message but as you can see, I'm new to this forum and unlike the pm on tripadvisor, there's no 'reply' button for dummies so I'm posting here again just in case the message did not go through.
To cover jiufen, jinguashi, shifen, then go along the coast eastward covering all the northeastern scenic parks, down to Yilan, Hualien then Taroko would require at least two days if you want to get out of the car to gawk at the scenery.Otherwise, in theory, one day would suffice as it porbably take only around 6-7 hrs from Jiufen to Taroko.If NE coast is not your priority, then you could also take the expressway connecting TP to Yilan, which takes only about one hour as compared to the 2-3 hrs along the coast.

My suggestion would be to do
Yieliu Geologic park --Peace island (this is a mini peninsula in Keelung, make a brief stop here , there's a vantage point where one could see the distant Keelung island and there're also various interesting rock formation there).--jiufen--jinguashi--Yingyang sea--Nanya coast--Bitoujiao (nose tip in Chinese)--Northeastern coastal scenic park--Fulong beach--Yilan , here you could make a detour to Jiaoxi Royal hotel to take advantage of their meal plus hot spring package--Chingshui cliff--Taroko tienxiang.

Like I said, We just did a similar journey over 3 days in the reverse order (minus the Taroko portion, of course, as we live in Hualien and has been there umpteen times).
I have just put up a hotel review for Jiaoxi Royal on tripadvisor Taiwan forum; my username on that forum is mariatan so if you are interested, you could take a look there to see what the Onsen is like.