Preliminary reminder: Any question which begins with "how can I make someone else do a thing" is properly answered with 'you cannot.' You cannot control other people's decisions and actions. All you can do is understand motivations and try to change incentives.
Also, I'm assuming here that you're American (since that was your comparison) and that you're not ethnically Chinese (since that would make this behavior seem really weird to me--in my experience the usual response for an Overseas Chinese person would be to expect them to speak Chinese, rather than insisting on using English--but who knows, people are strange).
Bad Approach
Maybe you're fed up. If you really want to get in this kind of contest, well--your boss wants to speak English with you? Just go right ahead and speak English to your boss. Speak the fastest, most jargony, most slangy, most indistinctly pronounced English you can manage. Dare him to admit he doesn't understand you. Ideally when other people are watching--really embarrass that guy. Keep it up until he finally code-switches at you.
Will you change his mind? No. But will you earn his respect? Also no. In fact you'll probably earn his eternal resentment: he'll probably fire you, which he'll probably put down to your (not his) inability to communicate. Then your Alien Resident Certificate will terminate, you'll have to find another job, leave the country to reapply for another visa, wait a few months without work until it's all set up, and all of that. But won't it feel good to know nobody disrespects your Chinese skills and gets away with it?
Smart Approach
Okay, so we've rejected Bad Approach as shortsighted and unhelpful. Let's see if there's something more productive that you can do.
First, a mind-setting reminder. You weren't hired to be a software engineer. You were hired to help your boss achieve his deliverables and maximize your company's revenue. If you can do that solely by being an excellent software engineer, hey, 恭喜恭喜. If your boss feels that you can best maximize value for your employer by having a chat in English, have a chat in English. Is he doing this because of potentially reductive or disrespectful stereotypes of you as a (presumably) non-Taiwanese face in the company? Maybe yes, maybe no, who knows. Even in the US there are many people who would say to grin and bear it; and this is more hierarchical than typical American work culture. Your best route to success at your job is to deliver excellent value for your company in a way that is obvious and makes your boss look good. You would absolutely be wise to make sure that your complete competencies--the value you bring to the company as a developer, as well as your ability to integrate culturally with your team--are visible both to your boss and to people with more authority than him (in a non-challenging way, of course).
But at the end of the day you are a foreigner in a country which does not have the long history of immigration that the US does. You're going to encounter people who make assumptions about you or have expectations of you. Many of those will not be flattering. Many of them are not going to go away just because they're unfounded or because you correct them. Pointing out how unfounded they are--well, you tried this; you asked a question and you got your answer. Further action of the kind you've been taking is likely to be read as antagonism on your part--antagonism that will not be viewed as you being righteous and justified, but as you not understanding local cultural norms of showing deference to your supervisor. Think of it as Bad Approach 2.0.
I mention this because, as an American who once strongly considered immigration to Taiwan myself, it was really important for me to realize that American acceptance of immigration (recent tide of nativism aside) is actually really unusual. The idea of cultural assimilation, especially, is really unusual. Pretty much every political perspective in the US assumes that at least some subset of people can come to America and "become American." That is not the case for other countries. It is entirely possible that in the future you will have lived in Taiwan for over half your life and you still won't be 'assimilated' or automatically accepted as 'Taiwanese'. Part of which will include people assuming you should speak English. This just has to be part of your calculus as you decide whether to continue permanent residence there.
You only get what you give
Mindset adjustment aside, you still find the current situation intolerable, and while I do think you need to reframe your perspective a bit, I don't want to dismiss the distress that you feel.
You might have more success changing behavior if you view this less as forcing your boss/that subset of your coworkers to change their behavior, and more on giving your boss specifically whatever it is he wants. One way forward (if it hasn't been compromised by going to HR) might be to try to talk with your boss more, in English. Initiate conversations--perhaps even outside of main work hours--where you know your purpose for engaging is to give him a chance to practice (or show off, whatever it is) his English skills. It's not really fair that you should have to do extra, but welcome to the immigrant experience. If you are going out of your way to accommodate him and give him free practice sessions/face/whatever he's looking for, it may be this will help him be more accepting of you the rest of the time, such that you can gradually move to using more Chinese in other of your interactions.
You might also be able to use Chinese more in workplace social events. Especially humor--if you know that what you're saying is funny--spend some time researching Chinese wordplay. (But I don't think at this point that the issue is them thinking you don't speak Chinese.)
Maybe your written interactions with him can include more code switching or saying things in both languages--you could even explicitly frame this as trying to improve your Chinese in order to have better communication with your colleagues (surely you know humility is the culturally valued approach here). Treat him like the expert (which, well, he is) and (occasionally) ask intelligent questions that emphasize his superior knowledge. Don't insist that he speak Chinese with you; treat it as a sometimes thing that he can do that's very helpful to you at low cost to him, so he can feel magnanimous. Will he eventually switch 100% of the time? Probably not. But you'll have a better and more successful relationship with him, while helping to emphasize one of the more unique skills you bring to this workplace.
Of course, it's also possible that it will become clear through this that he's speaking to you in English because his English is better than your Chinese. Who knows. If that's the case, well, you've learned something else--maybe not what you wanted to learn, but something useful anyway. But if you approach this as someone who's humbly looking to improve, you'll probably see a lot more response than by making demands or going to HR.
