How do I make my yoghurt tangier?

For a tangier yoghurt be sure to use the Tangy Yoghurt culture.

The longer you ferment your yoghurt, the tangier it will be, up to a point. Fermenting for 18 to 24 hours will give you a tangier yoghurt than fermenting for 8 to 10 hours. After fermenting for 24 hours, the milk sugars are starting to run short, slowing the bacteria growth and the production of lactic acid, the compound that gives yoghurt that tangy flavour.

If you are using tangy yoghurt culture, and you are fermenting for 24 hours, and you still want more tang, try adding a small amount of sugar, giving the bacteria more to eat, thereby creating more lactic acid.  This is a balancing act. Too much sugar and it will be too sweet. Start with just a little sugar, like ¼ of a teaspoon and a few more hours of fermentation should give you a tangier flavour.