The required level for promotion differs for each batter grade.

Normal - Lvl. 10
Minor - Lvl. 7
Major - Lvl. 6
Allstar - Lvl. 5
Legendary - Lvl. 4

These are the minimum required levels to promote the batter and you can promote the batter at any level above the minimum.

Promoting the batter at a level above the minimum will retain the level of the batter.
Promoting batters require gold.