Misleading title. Beggar So (the titular Drunken Master) is the central character, but the story doesn't say much about him !
Beggar So is trying to keep his two star students, brother and sister team Cheong and Gam Fa, in line and well-trained. But So's old enemy Grasshopper Bill Chan and his brother Cougar cause trouble. Bill helps young Kai to be pledged in marriage to Gam Fa against her wishes, but actually plans to have her for himself.