Korean · Pronunciation Guide
dwe-da. The first block is one syllable with a w-glide onto an 'eh' vowel, not the 'oy' of 'boy' that the romanized 'oe' suggests.
doeda
Both syllables carry the same weight. The dictionary form is not what you will actually say -- 돼요, 됐어요 and 되고 are the everyday shapes -- and in 돼요 the vowel contracts further, so it repays hearing the citation form and the conjugated one side by side.
Listen: 되다
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의사가 되고 싶어요.
Uisaga doego sipeoyo.
I want to become a doctor.
Listen: 의사가 되고 싶어요.
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의사가 되고 싶어요 keeps the ㅚ intact in 되고 and then follows with 싶어요, where the ㅍ resyllabifies forward to give si-peo-yo. Note also that 의사 begins with the full ㅢ diphthong, because it sits in a word-initial syllable, unlike the possessive particle 의.
Reading 'doe' as English 'doe' or as 'doy' are the two failure modes, and both miss the glide. Round first, then spread: it is w plus e, compressed into one beat. Learners also aspirate the initial ㄷ into 'twe', which sends the word toward 퇴 -- the plain consonant should carry no breath behind it.