Start by attacking the stations nearby, aiding the rebel fleets. Wait until at least one or two stations are destroyed, then send the shuttle. I sent it above it, so even though it took longer, the enemy were too distracted with the other ships to focus on the shuttle. Once the shuttle gets near, it should start the capturing sequence.
Oh, and whatever you do, you'll want the eclipse to have as much health as possible, so don't attack it.