28" around and 12" tall - LED strips are very light, if your pet doesn't mind putting the tank top on the weight of a few LED strips will not be noticeablle.
The 12V battery pack to drive the LEDs will weigh more.
One option for you is to wire the LEDs in a 9x9 array.
9 output pins with current limit resistors from a 20 IO pin arduino will drive the rows of anodes high.
9 output pins from the arduino will drive the columns of cathodes low.
To run the matrix from 5V and without using any external hardware (i.e. shift register), you will only drive 1 anode high and 1 cathode low at a time to turn on each LED.
If the ontime for each LED is limited to 500uS, then the entire matrix can appear to be on all together thru Persistence of Vision (POV):
(1 frame/81 LEDs) * (1sec/24 frames) = ~514uS/LED.
That leaves the Rx/Tx pins free to do other stuff, like downloading new test code.
So your code can either drive 1 anode line, and cycle thru the 9 cathodes, or it can drive 1 cathode and cycle thru the 9 anodes. Either sequence will result in just 1 LED being on at a time.
I don't know which particular Lilypad supports all the to allow this. We have a protosnap and it doesn't make all 20 IO pins available.
I have some 328 SMD boards which are small and could do this also.http://www.crossroadsfencing.com/BobuinoRev17