The heat in Chittaurgarh can be torturous and one would need sufficient sun protection such as shades and caps. It would also do to bring along a sunscreen lotion for those with delicate skin to avoid heat burn. Wear a strong pair of shoes while climbing the Chittaurgarh fort to avoid getting hurt and spraining ones ankles.
The monkeys at the fort generally do not harm anyone but always keep a safe distance as they are unpredictable creatures. Besides be careful while resting under a tree as some monkey sitting above might just drop their excreta on you!
The fort is massive and hiring bicycles would ensure that your exploration of the place is not as tiring. One could get lost in the fort, so make sure that you travel in groups and with local guides.
