You utterly fail at saving the world, the bad guy successfully triggers the apocalypse, which takes the form of thousands of giant white baby monsters, apparently lead by a giant pregnant women made of salt devouring, everything around them, including the remainder of your party (which consists of an old racist priest, a child serial killer, and a pedophile)...
In ending D, after realizing the situation is well and truly hopeless, you decide to send your remaining companion in on top of the giant pregnant women to activate his power to stop time. He achieves this (while you are slowly and painfully eaten alive by the babies, thereby freezing all time in the immediate area and possibly averting the apocalypse...
In Ending E, you instead decide to kick the shit out of the demon woman, and through the efforts of your final companion, you manage to send her running. You pursue it into another dimension, which turns out to be modern day Toyko, defeat it through a rhythm-based minigame (which is the first and only time you have to do a rhythm minigame in the whole game), and once you have successfully killed it, are promptly shot down by the Japanese airforce...
It's also revealed that the final ending listed above directly resulted in the apocalypse situation which lead to the events of Nier, a later installment in the series, which also ends with humanity irrevocably on the road to extinction.
Literally the best ending to Drakengard 3 is the one which ensures that absolutely none of the events of the other games in the series can take place.
