Dietrich went in with all of the other marines to investigate the colonists' locator beacons, which we learn are all in one place under the reactor cooling tower in the alien "nest".
After the marines discover a cocooned colonist and kill the chestburster who kills that colonist, the aliens attack. Most of the marines die, but Ripley saves Hicks, Hudson, and Vasquez (Bishop and Gorman are in the APC during the battle, Farro and Spunkmeyer are on station in the dropship outside the complex).
After they escape the nest, Hudson looks at the command consoles in the APC:
HUDSON: The sarge and Dietrich aren't dead, man. Their signs are real low, but they ain't dead.
A brief argument ensues about whether to attempt a rescue, which Ripley ends:
RIPLEY: You can't help them! You can't. Right now they're being cocooned, just like the others.
So while we don't see Dietrich die, she was almost certainly killed by a chestburster after being cocooned and impregnated, along with Apone.