This is the audio exerpt of ɚ spoken within a word. It may sound a little short or unclear, but that's exactly how it's in the real context. For more details, read the below explanation of pronunciation and listen example words that contain ɚ by pressing the word buttons.
1. Open your mouth for about 50%.
2. Relax your lips.
3. Raise the center of your tongue without touching the palate.
4. Push air from lungs while vibrating vocal cords.
5. In the end of the pronunciation, move the tip of your tongue towards the point above the alveolar ridge but without toucing it.