I work for a medical laser company and I threw this one out to my boss who is a senior scientist. He feels that in order to accomplish what you're describing it would require a laser with a power level in the megawatts. He also doubted if enough energy could be focused on the target due to the impurities in both the aquarium glass and the saltwater and to overcome the thermal dissipation that would occur from the water. With enough power to kill the target you'd vaporize the water the beam passed through causing a really interesting reaction within the aquarium.
Steve had the best idea with using a tube to minimize the distance the laser would have to travel through water. That way the final lens could be fractions of an inch from the target. It would still be very dangerous with the scattered light and would probably blind everything in the tank that has eyes.
I suggest investing in Joe's Juice or a CBB for aiptasia control.