I would like to know the list of diphthongs and hiatuses in Brazilian Portuguese. Because I need the correct syllable division.
As spelling is concerned, diphthongs and hiatuses are the same in Brazil and Portugal; there are some differences in pronunciation. I’ll focus on spelling and the “official” syllable division, which determines where you can hyphenate a word, but include some notes on pronunciation and examples with audio links where you can hear native speakers pronouncing the words; I indicate syllable division with a dot.
Falling oral diphthongs ― vowel + i or vowel + u:
Falling nasal diphthongs
Phonetic diphthongs you wouldn't guess from spelling. There are nasal phonetic diphthongs in end-of-word -em as in vem or tam.bém, pronounced [ẽj]; [ɐ̃j], rhymes with mãe, in central and southern Portugal. End-of-word -êm, as in têm, is [ẽj] in Brazil, and the double diphthong [ɐ̃jɐ̃j] in much of Portugal. End-of-word -am is as ão, [ɐ̃w], as in fo.ram. In Brasil too end-of-syllable l is usually vocalized into [w], creating phonetic diphthongs. Hence the al in Na.tal is pronounced /aw/; the ol is sol as /ɔw/ ― this diphthong /ɔw/, with an open o, does not exist otherwise in Portuguese language (ou is always /ow/, closed o, or reduced to the monophthong /o/).
Rising diphthongs starting with u occur after g and q in words like á.gua, qua.tro, a.guen.tar, tran.qui.lo, ar.guir*, quó.rum. This is not universal though: the u in these ui and ue is silent in many such words, like es.qui.lo, ma.la.gue.ta, etc. If you do not know, the only way is to look up a dictionary that shows pronunciation, like Michaelis (Brazilian standard), Priberam (you can select Brazilian or European standard) or Infopédia (European standard).
There are true hiatuses in Portuguese such as aé in a.é.ria and ií in fri.í.ssimo, that is two adjacent vowels that belong to different syllables (dot shows syllable separation), and are therefore pronounced separately, not as a diphthong. But then there lots of “official” hiatuses that are undone in standard pronunciation. This can vary a great deal between Brazil and Portugal, and within Brazil itself. For instance, leão has officially two syllables and a hiatus, le.ão, but the Portuguese and many Brazilians turn the e into the semivowel [j] and pronounce the word as the triphthong /ljɐ̃w /; in Portugal this is the standard pronunciation, as shown in dictionaries such as Infopédia. The same goes for pra.te.a.do, where e.a is “officially” a hiatus, but is pronounced as the rising diphthong /ja/; in Forvo one Brazilian pronounces it as a diphthong, another as a hiatus. Now this is pronunciation. Official orthography has them as hiatuses, which means that you can hyphenate the word there at the end of a line (le- ão, prate- ado, although some such hyphenations are discouraged anyway).
So I’ll now follow the spelling and show official hiatuses regardless of whether they are pronounced as hiatuses or not. And I’m pleased to announce that off all possible twenty-five pairs of vowel letters, twenty-four can be found as hiatuses in words recorded in dictionaries, and the twenty-fifith can be found in a word not recorded in dictionaries. One pair, say i.a, can appear in several different hiatuses, because the hiatus may be formed of just the two letters (pi.ano), or each of the letters may be part of a diphthong (pi.ão, boi.a, boi.ão), the second vowel may be nasal (cri.ança), and so on. I’ll group the examples according to the two letters on either side of the hiatus, and highlight in boldface all the letters that belong with them, as in the examples above.
How can you tell whether two vowel letters make a diphthong or a hiatus?
You can in most cases when the main stress is there. Compare pais and país: the accented í tells you that it is a hiatus, pa.ís, and that the i is the stressed vowel, whereas in pais, ai is a diphthong. The same with saúda, ruído, etc.: the two adjacent vowels make a hiatus, and accent shows the stressed vowel; similar sequences with no accent, like cauda, cuido, have diphthongs.
Exception. No accent is used if the second vowel is followed by l, m, n, r, or z, and makes a syllable with it; that vowel is still stressed and it is a hiatus though: pa.ul, Co.im.bra, a.in.da, ru.ir, ju.iz. Note that these consonants must belong to the same syllable with the preceding vowel: Ra.ul (hiatus), but Pau.lo (diphthong), because in Paulo the l forms a syllable with the following o, not the preceding u. No accent is used either if the second vowel is followed by nh: ra.i.nha.
Another exception. So far we’ve relied on stressed diphthongs not requiring accents. But they do in the third-to-last syllable: te.ra.pêu.ti.co. How can we tell it is not te.ra.pê.u.ti.co. Well, I don’t know this is a general rule, but the only hiatuses that I know of that are accented in the first vowel are é.o (al.vé.o.lo), í.a (trí.a.da, Lu.sí.adas) and í.o (va.rí.o.la, pe.rí.o.do, mí.o.pe), and there is no diphthong eo, ia or io (remember, oral diphthongs are vowel + i/u, or follow the pattern qu/gu + vowel). So it is safe to assume that anything like êu is a diphthong. We also put an accent on diphthongs éi, éu and ói at the end of a word (including monosyllables): pa.péis, cha.péu, véu, sóis, cons.trói, so that we know the accented vowel is open, not closed. Again, this does not fit the pattern é.o or í.o.
The real problem is in unstressed syllables. For instance, it is cui.da.do, but ru.i.do.so; we cannot, as before, put an accent on the i of the hiatus, because it is unstressed; the stressed syllable is do. Same with rei.fi.car and de.i.fi.car; reumático and re.uni.do. So any pair vowel + i/u in an unstressed position could in theory be a diphthong or a hiatus. If you do not know, the only way is to look up a dictionary that shows syllable separation, like Aulete , Michaelis (Brazilian standard), Priberam (you can select Brazilian or European standard) or Infopédia (European standard).
If you really just want the list of diphthongs, then the Wikipedia article on ditongos shows a list of the existing diphthongs: https://pt.wikipedia.org/wiki/Ditongo
They're not organized, but they're there.
But you should consider the points raised by Jacinto and Schilive in the comments to your question.
If what you are looking for is to split words into syllables occasionally, the Priberam online dictionary splits the words into their syllables.
See e.g. Priberam splitting "bolacha" into its 3 syllables:
"bolacha", in Dicionário Priberam da Língua Portuguesa [em linha], 2008-2020, https://dicionario.priberam.org/bolacha [consultado em 14-12-2020].
If what you want is an exhaustive list of diphthongs, a quick internet search will provide you with many results even if you search in English, such as https://www.learningportuguese.co.uk/guide/pronunciation/diphthongs
Wikipedia has plenty of information on this, both in Portuguese (more specific and with sillabary examples) and in English (more technical, with IPA notations and few examples).
Note that there are also some triphtongs (tritongos), even if they are rare: U·ru·guai, quais·quer, etc.
The Wikipedia article on triphthong mentions portuguese examples.