I've heard there are also other ways of tiering up such as beating a higher-tier player in a H2H or match play, but this is how I summarize it based on my experience :
HACK to AMATEUR
Minimum Ranked Rounds : 5 / Average Score : 100 or lower
AMATEUR to PRO
Minimum Ranked Rounds : 10 / Average Score : 80 or lower
PRO to TOUR PRO
Minimum Ranked Rounds : 20 / Average Score : 72 or lower
TOUR PRO to MASTER
Minimum Ranked Rounds : 25 / Average Score : 67 or lower
MASTER to TOUR MASTER
Minimum Ranked Rounds : 40 / Average Score : 63 or lower
TOUR MASTER to LEGEND
Minimum Ranked Rounds : 50 / Average Score : 61 or lower
LEGEND to TOUR LEGEND
Minimum Ranked Rounds : 500 / Average Score : 60 or lower
TOUR LEGEND to CHAMPION
Minimum Ranked Rounds : 7501 / Average Score : 59 or lower
(1 Increased the number from 200 on December 19, 2018)
CHAMPION to TOUR CHAMPION
Minimum Ranked Rounds : 1,0002 / Average Score : 55 or lower
(2 Confirmed as of January 14, 2020)