Chinese · Pronunciation Guide
joo-yi: a low sagging first syllable with the tongue curled back, then a weak toneless second.
zhǔyi
Dip then nothing. The neutral second syllable insulates zhǔ from anything on the right, but the left edge is exposed — and since ideas are usually described as good ones, the adjective 好 in front is itself a dipping tone. That is exactly the situation in the example sentence.
Listen: 主意
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我有一个好主意。
Wǒ yǒu yí ge hǎo zhǔyi.
I have a great idea.
Listen: 我有一个好主意。
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我有一个好主意。 has two separate events. Wǒ and yǒu are adjacent dipping tones, so wǒ rises. Then yí is the converted 一 before the underlyingly-falling ge. And hǎo and zhǔ are also adjacent dipping tones, so hǎo rises: háo zhǔyi. Two conversions and one 一 change in seven syllables.
The retroflex flattens into an English j, pulling the syllable toward jǔ. Curl the tip back. Restoring a falling tone to yi is the other error, since 意 carries one as an independent character. And the hǎo zhǔ conversion crosses from an adjective into a noun, which is precisely the kind beginners overlook.