If you want to unlock new Wung Fu abilities, you will need to get what are called Upgrade Points in Biomutant. The main in which you can get these points is by leveling up from gaining tons of XP. That said, you can level up fast by farming quests in the game - doing this will also give you ample time to earn some decent loot and crafting materials.
Another way you can earn upgrade points from finding objects in the game and examining them along with levels. These can be anything from books to other items, so we highly recommend exploring the world.
Related: How to level up fast in Biomutant
However, you will usually need to defeat a squad of enemies and a small boss to get them. These are called lair fights, and after you finish them, you can also find various chests that can often reward you with one upgrade point. Once you get upgrade points through whatever means we have listed here, you will be able to unlock Wung Fu abilities by visiting its skill tab.
Along with Wung Fu abilities, you can also use these points to unlock new skills, such as ones for weapons. So what are you waiting for? Get out there now and start earning these upgrade points!