Ok so I got this achievement the 2nd time I played Portugal so either I got extremely lucky or the 500+ hours I put into HOI4 paid off. I will write this guide in short form with the assumption you have put in a similar number of hours and know how to create a good template and use CAS, etc.
Having a Kaiser Germany makes it easier, id recommend restarting if Germany goes for the Rhineland.
Also you will have to play late game (finished 1951) AND will have to fight most of the world, like for most of these achievements.
Your puppet MUST have a capital in Macau, and must include modern China. Taiwan IS required. Mongolia and Korea are NOT required.
First thing rush the focus to get the monarchy. You instantly become a major once you unify with Brazil. More on this later
Around 1936 or 37 you should start seeing pop ups for collaboration governments (must have DLC) with 2 options "they have our blessing" or "they are not yet ready" you want to select "they are not yet ready for all" EXCEPT for the one in China. If you accidently press "they are not yet ready" you can go into decisions and select "create a collaboration government in China" youll know you did this right when you get a puppet called "Portuguese China" or something like that with a capital in Macau. This is a MUST to get the achievement.
Once you do "the return of Duarte" check your stability you should have around 60 or 70. This will determine the focus you do next. This is because if you select "restoration of the monarchy" and your stability is under 50% it WILL trigger a civil war. This will be extremely hard to win and what caused me to fail the first playthrough.
If your stability is 60 or more rush "promote the monarchist cause in Brazil" and "restoration of the monarchy" but make sure to check your stability before doing the second one. If you do this fast enough you will be able to avoid a civil war and become the Portuguese empire. Now you do "monarchist uprising in Brazil" and "The empire of Brazil" to trigger the unavoidable but easy Brazilian civil war. Now just do the focus "the kingdom reunited" THIS IS THE EASIER WAY
If your stability drops below 40% dont worry you CAN still win. Just do the other focuses namely "monarchist uprising in Brazil" and "The empire of Brazil" as this will cause a civil war in Brazil. This civil war is always unavoidable however it is very easy as the rebels you are allied with always outnumber the government and you can send your troops to help. Once that happens rush "promote the monarchist cause in Brazil" and "restoration of the monarchy" and just hold a defensive line during the civil war while you research "the kingdom reunited" and youll merge with Brazil. Using their army should help you win the civil war but itll still be hard as the rebels have a good defensive line around Porto.
Congrats on forming the Porto Brazilian Empire. Your macau territory should now be called Porto Brazilian China or something similar, thats ok as long as the capital stays in Macau. We will focus on China later we will need to build up Portugal first.
Now start doing the focuses under the "continue the public works" focus. These will rapidly build up your economy by giving you civs and military factories.
Around this time the Spanish civil war should have ended or is close to ending. Research "Remember Olivenca" as this will give you claims on Spain. Once they finish the civil war declare war on them, they will basically have no army and should fall quick. Annex it all you need the territory trust me.
At this point I got lucky. I was in an Alliance with a non aligned Germany, UK, Italy, Mexico and Japan (among some minors) vs France, USA, Russia, and China (plus some minors). I took France first fairly easily, than went after the balkans. Germany was pushing against Russia in the west while me and Japan swept up China and that Russia from the east. UK also launched uprisings in the former colonies including Canada.
Using Mexico from the south and Canada from the north we quickly wrapped up the US and that was GG. Somehow I had the largest warscore by FAR (around 2200 or more) and was able to quickly secure most of China and gave it to my colab government. I also made a puppet from Russia, and the USA.
Now I had 2 issues. UK owned Hong Kong and Japan owned Taiwan and several other states in China as well as its 2 puppets. I would have to defeat them now.
I went after Japan first. the massive UK navy destroyed the Japanese Navy while my troops seized Taiwan and their mainland territory. Upon gaining naval superiority we launched into Japan. Also I had to use LOTS of nukes (sorry Japan). Upon beating them I gave their mainland territory and Taiwan to PB China and made Japan a puppet.
Finally the UK, they actually were pretty easy. Their African colonies fell, India was surrounded so they fell quick, and Germany actually successfully naval invaded London. They well very quick and I snatched up Hong Kong. Achievement popped after the peace deal.
If you guys want more detail or clarity just comment below.