Hi May I know how can I go Kaoshiung from taoyuan airport?

No direct bus can take you from Taoyuan Airport to Kaoshiung.
Upon landing, you can take shuttle bus to get to Taipei Bus/High-speed Station. The duration is about 55 mins. It costs NT$125 per person.
Then transfer to the bullet train to Kaoshiung. The train schedules are from 06:30 to 23:00. It takes around 20 mins. The ticket fare is NT$ 175 per person.