When we have a long, convoluted sentence with a lot of commas, a really useful trick is to eliminate all of the parts of the sentence set off by commas. Anything set off by commas should be extra, descriptive information and shouldn't be grammatically necessary to the sentence. So once we cut out all of the stuff set off by commas, we should be left with a complete sentence. If we don't have a complete sentence, there's something wrong with the sentence structure of the answer choice, and we can eliminate.

(A) Weighing more than 300 pounds and standing over 2 meters tall, the flightless bird Titanis walleri, which lived in Florida about 2 million years ago and may have evolved opposable thumbs to subdue struggling prey, is the most fearsome representative of the aptly named "terror birds."
(A) The flightless bird Titanis walleri is the most fearsome representative of the aptly named "terror birds."
This is a complete sentence. We'll keep it.

(B) The most fearsome representative of the aptly named "terror birds," the flightless bird Titanis walleri, which lived in Florida about 2 million years ago and may have evolved opposable thumbs to subdue struggling prey, weighing more than 300 pounds and standing over 2 meters tall.
(B) The most fearsome representative of the aptly named "terror birds" weighing more than 300 pounds and standing over 2 meters tall.
This isn't a complete sentence. Eliminate.

(C) The most fearsome representative of the aptly named "terror birds," the flightless bird Titanis walleri weighed more than 300 pounds, stood over 2 meters tall, having lived in Florida about 2 million years ago and may have evolved opposable thumbs to subdue struggling prey.
(C) The flightless bird Titanis walleri weighed more than 300 pounds, stood over 2 meters tall, having lived in Florida about 2 million years ago and may have evolved opposable thumbs to subdue struggling prey.
This doesn't seem like an incomplete sentence, but we might notice a parallelism issue with our list at the end:
The flightless bird Titanis walleri
-weighed more than 300 pounds
-stood over 2 meters tall
-having lived in Florida about 2 million years ago
-may have evolved opposable thumbs to subdue struggling prey
"Having" doesn't match the grammatical structure of the other list items, so our list doesn't have correct parallelism. Eliminate.

(D) Weighing more than 300 pounds and standing over 2 meters tall, the flightless bird Titanis walleri lived in Florida about 2 million years ago and may have evolved opposable thumbs to subdue struggling prey, the most fearsome representative of the aptly named "terror birds."
(D) The flightless bird Titanis walleri lived in Florida about 2 million years ago and may have evolved opposable thumbs to subdue struggling prey.
This is a complete sentence. However, if we go back to our original sentence to see what the second piece of descriptive information described, we see that it's closest to the noun "prey". We know that modifiers (descriptive info) must describe the noun they're closest to, so this sentence is describing the Titanis walleri's prey as being the most fearsome "terror bird". This doesn't make sense - we want to describe the Titanis walleri as the most fearsome "terror bird", not the things it eats. Eliminate.

(E) The flightless bird Titanis walleri, which weighed more than 300 pounds and stood over 2 meters tall, lived in Florida about 2 million years ago and may have evolved opposable thumbs to subdue struggling prey, the most fearsome representative of the aptly named "terror birds."
(E) The flightless bird Titanis walleri the most fearsome representative of the aptly named "terror birds."
This is not a complete sentence. Eliminate.

This leaves us with answer choice A as the correct answer.