All parts of this plant contain tropane alkaloids (and most notably atropine and hyoscine), although the roots and berries are the most TOXIC parts.
Some types of livestock and rabbits are said to be able to eat Deadly Nightshade with no ill effect (rabbits and goats possess the enzyme atropinesterase which neutralise the effects of Deadly Nightshade), it is harmful to humans and many domestic pets. It has been labelled as one of the most TOXOC plants in the Eastern hemisphere, and it is known that a child died from eating two berries.
Symptoms of poisoning include sensitivity to light, blurred vision, loss of balance, hallucinations, delirium, convulsion, and possibly death.
While we do not know its effects on reptiles, we would definitely recommend that you do not allow your tortoise to come into contact with this plant, or any area where its leaves or berries have fallen to the ground.