Transmission not shifting into all gears?

That car has what is called a DSG (dual shaft gearbox) that means it basically has one clutch that selects one set of gears and a second clutch that selects the other set of gears. In your case it sounds like the second clutch isn't operating. Unfortunately, that gearbox is also a known problem item because of its design and being less able to handle the engine's torque during "spirited" driving. The first step though is going to be to use a scan tool, which has bidirectional control, to look at the transmission control system and use it to test the clutch activation systems to see if the issue is in the transmission controls or if it's a failure in the clutch mechanically. The latter is common and generally requires that the mechanical clutch assembly be replaced due to physical damage.