As per the film genre, the main characters engage frequently in hand to hand combat. Po and his friends fight primarily empty handed, while the villains often use weapons.

Some characters are presumably 'killed' in the movie, most explicitly concerning a villain's henchman is stabbed when he refused to fire on his own troop.

To thwart a prophecy, Shen leads a genocide of pandas.

Po has a nightmare about his parents replacing him with a radish, and that radish is tormenting him. This may disturb young viewers.

It's relatively dark and violent.

The flashback scene is quite disturbing, especially since it comes pretty much out of nowhere.

Quite a bit darker than the first Kung Fu Panda, with themes of: genocide, anarchy, and revenge.

Spoilers ahead: