I'm still an amateur and always had problems with this, got some advice from an experienced jazz pianist I know. His suggestions were roughly to:

1. Start by transcribing the root note that you hear

2. Go back and see if each chord sounds major or minor - most of the time that will give you a major/minor third

3. Go back and play the 5th, and see if it sounds right - most of the time it'll be there

4. Don't worry about 7ths/9ths yet, they'll come, but give them a go

5. Once you've got a few chords, try and figure out the key, and that will help figure out others

So he was basically suggesting to transcribe by each note's function in a chord, starting with most -> least important. It still needs some music theory of course, but doesn't need you to listen to an entire complex chord at once.