How do turbochargers aid engine performance as density altitude increases?
An oversimplification for sure: Turbochargers essentially compress the air going into the engine (cylinders) to maintain (near) sea level pressure internally, so the external density altitude doesn't affect the performance of the engine.  

The "liability" at low density altutudes is that it is possible to over-boost the engine, potentially damaging it. See the related question for more in-depth explanation and the liability of having a turbocharger at low density altitude.