Some 15 tortoises, valued at £125 each, three geckos, worth £50 each and two orchid mantises worth £44 were taken from the Fin Room on Albert Street on Friday.
In a statement posted on their Facebook page, pet shop’s owners wrote: “We were broken into last night and all our tortoises are gone, these were for people and children's Christmas.
“We have caught the two men on camera that were in the shop yesterday – police are involved. They have trashed out reptile room and broken the window.
“They have left animals outside in the cold to die, we are doing all we can to save them.
“They have also took three leopard geckos, a fan foot gecko, 15 tortoises, and also three orchid mantis have been stolen too.
“We can't let these horrible people take anything else from us.
“The support we have been offered from everyone has overwhelmed us. I thank you all from the bottom of my heart.”
Police say they are treating the break-in at the Albert Street establishment as “deliberate and targeted".
Inspector Hugh Burns said: “We need to find these animals as soon as possible as they could suffer harm or even die due to being away from their normal, warm environment.
“I would appeal to anyone who has been offered these animals or who knows anything about them being offered for sale to get in touch.”