Very few people seem to know it, but there is a thing called Taiwanese Bopomofo (臺語注音符號), or more accurately Taiwanese Bopomo, as the “f” sound does not exist in Taiwanese. This phonetic alphabet allows you to efficiently transcribe the pronunciation of Taiwanese Characters. I’m going to teach you Standard Taiwanese Bopomo, but there are also four extra letters available to transcribe some Taiwanese dialects, but I won’t be looking at them here.
In this short article, I’m going to show you in a few steps how you can master Taiwanese Bopomo if you already know Mandarin Bopomofo, and if you already have basic knowledge of spoken Taiwanese, as I won’t be explaining Taiwanese pronunciation, you need to already know what’s a voiced consonant, nasal vowel, etc. But you can easily access the following dictionary that allows you to enter any character with Taiwanese Bopomo annotations and audio, for you to get more familiar with Taiwanese sounds.
First, take out your Mandarin Bopomofo and remove all the letters representing sounds that do not exist in Taiwanese, shown here in red. Good job, you already know more than half of the Taiwanese Bopomo.

Then, create the voiced equivalents (濁音) of ㄅ, ㄍ, ㄐ, ㄗ by adding a little loop at the end, creating the letters ㆠ, ㆣ, ㆢ, ㆡ. Aren’t they adorable?

Now, creates the nasal equivalents (鼻音) of ㄚ, ㄞ, ㄠ, ㄧ, ㄨ by also adding a little loop at the end, creating the letters ㆩ, ㆮ, ㆯ, ㆪ, ㆫ. Besides, you will now learn two completely new letters; ㆦ[ɔ] and ㆤ[e], and their nasal equivalents; ㆧ and ㆥ.

Here comes the Mmm letters. That’s not really their names, I just came up with it. We already have a “m” sound ( ㄇ ), so why new letters? Well Bopomo (and Bopomofo) has the particularity that it doesn’t want letters to have multiple roles. You see, in Taiwanese (just like in Mandarin) every syllable is composed of initials, medials, and finals. Each letter can only be associated with one role*. ㄇ has already been attributed the role of an initial, meaning that it cannot be used to end a syllable. Therefore, we need new letters to express the three final “m” sounds. The first letter is ㆬ which is simply a “m” sound, just like ㄇ . The two other letters are a combination of the first letter and the letters ㄚ, ㆦ, to create the letters ㆰ[am], and ㆱ[ɔm].

Then we have the Ng letters, which are the hardest to pronounce in my opinion. ㄫ is the initial, while ㆭ is the final. ㆲ is a combination of the sound ㆦ and [ŋ] (ng). Note that when the sound [ŋ] is combined with the medial ㄧ, then we use the letter ㄥ, just like in Mandarin.

Last but no least, the tones. This is the most difficult part for me as I still have trouble distinguishing them. Taiwanese has 7 or 8 distinct tones depending on the source, two of which are created by “Tail Vowels”, which are represented in Bopomo using the letters ㄅ, ㄉ,ㄍ, ㄏ placed of the right side the syllable’s final for the 4th tone, and the same letters but with a dot on top for the 8th tone.

Let’s clean it up, and Tadaaa! Here is your full Taiwanese Bopomo alphabet (without the tones). Isn’t it beautiful?

This is how my Taiwanese notes look like, annotated with Bopomo.
Taiwanese is such a beautiful language, and I hope that the Taiwanese government could promote the use of Taiwanese Bopomo so that more people can be aware of the incredible linguistic capabilities that it has to offer, and I hope that somebody will one day come up with a Bopomo Keyboard.
I also highly recommend the online Taiwanese dictionary of the Ministry of Education. All its entries are annotated with Bopomo.
* ㄧand ㄨ are an exception in Taiwanese. They are both medials, but they actually can be used together in the same syllable, meaning that one keeps the role of medial, while the other will become a final