Longest reverse palindromic DNA substring
Pyth, 37 36 28 24 bytes
ef&amp;}TzqmaCd6T_mx4aCk6Tyz

Combining the tips from FryAmTheEggman and the reverse palindrome check trick from Peter, this is a super short version.
However, this only works with Pyth 3.0.1 which you can download from this link and run like
python3 pyth.py -c &quot;ef&amp;}TzqmaCd6T_mx4aCk6Tyz&quot; &lt;&lt;&lt; &quot;ATTCGATCTATGTAAAGAGG&quot;

(linux bash only. On windows, press Enter instead of the &lt;&lt;&lt; and then type the input)

This is my previous submission - 28 bytes solution
J&quot;ACGT&quot;ef&amp;}TzqTjk_m@_JxJdTyz

Thanks to FryAmTheEggman for this version. This one creates all possible subsets of the input DNA string, filters the subsets on the condition that the subset is a substring of input and the reverse of transform is equal to the subset itself.
Due to all possible subset creation, this takes up even more memory than Peter's answer.

This is my first submission - 36 byte solution.
J&quot;ACGT&quot;eolNfqTjk_m@_JxJdTm:zhkek^Uz2

This is the exact translation of my CJam answer. I was hoping that this would be much smaller but turns out that lack of translation method made it almost similar size (still 2 bytes smaller though)
Try it online here