This SC question is mostly about parallelism.

A. are serving the colony by tending juveniles, gathering food, building the nest, or they battle

There are two issues in this one. First are serving is not parallel to reproduce.

Also, there an issue in the last element of the list. If we remove all of the elements but the last we get the following, which does not work.

are serving the colony ... by they battle

B. are serving the colony in that they tend juveniles, gather food, build the nest, or battle

In this one, the use of in that distorts the meaning, causing the sentence to convey not that certain individuals serve the colony by doing certain things but instead that they can be said to serve the colony because they do certain things.

Also, once again, are serving is not parallel to reproduce.

C. serve the colony, tending juveniles, gathering food, building the nest, or by battling

In the version created using this one, the rest serve the colony, tending, ... incorrectly conveys that the individuals who reproduce do not serve the colony.

Also, prepositional modifier by battling is not parallel to participle or verb-ing modifiers tending, gathering and building.

D. serve the colony by tending juveniles, gathering food, by building the nest, or by battling

gathering is not parallel to by tending, by building and by battling. Alternatively one could say that the use of by before building and battling makes the sentence needlessly wordy.

E. serve the colony by tending juveniles, gathering food, building the nest, or battling

In the version created using this one, the meaning is clearly and correctly conveyed via the use of logically constructed parallel lists.

The correct answer is E.