Drunken Tai Chi tells the story of a troublesome young man named Ta Sha who rides a bike around town spoiling and ruining for others. But soon Ta Sha is confronted by his rival, the spoiled Chan Chuen-Chung who ends up fighting and humiliating Ta Sha in the process.
This leads to Ta Sha plotting a revenge on Chung with the help of his friends by setting up an ambush and using fireworks to their aid. However, Chung - accompanied by his brother Yu Ping - manage to walk away from the ambush and use the gang's weapons against them.
But as Chung is about to use fireworks on Ta Sha, Yu Ping makes Chung spare and let Ta Sha go. But Chung accidentally lights a set of fireworks resulting in Tai Sha getting heavily injured.
Devastated and angered by Chung's actions, Ta Sha's vindictive father hires Iron Steel, an infamous assassin, to wipe out Chung and his entire family. Iron Steel closes in on the family and kills everyone on sight.
Fortunately, Chung is present elsewhere and - after finding out that his family were killed while their house burned down - wanders around town in great grief.
Later on, Chung meets a puppeteer who takes Chung in and introduces him to his wife. After escaping a few more times from Iron Steel though, the puppeteer reveals himself as a master of tai chi and teaches Chung the art to counter Iron Steel's intense techniques and defeat him.
Eventually, Chung discovers that his family didn't die in a fire but were murdered by Iron Steel who was hired by Ta Sha's father. This determines Chung to seek out and face Ta Sha's father and Iron Steel once and for all.