Well, this is not a recommendation to do Hampi in a day. It's impossible, to say the least !
Nevertheless if you you are in a situation where you have only a day available, let's see how to take the maximum out of it. See here a more relaxed, 3 Day Hampi Itinerary.
We're going to discuss two possible itineraries here. Look at these and pick the one that interests you. You can even go bit creative with both, based on your interest, stamina(!) and the mode of transport.
Let's first start with the mode of transport. You can do it on foot, rent a bicycle or moped, hire a auto-rickshaw/tonga/taxi. All has its advantages and limitations. Mopeds (available for rent near Virupaksha Temple and Virupapur Gadde area). Be prepared and do not spend (waste) time searching for one. Remember we're about to cover 10-12 points of attractions in a day!
For the sake of convenience , the attractions are discussed based on its proximity.
Group 1: Hemakuta Hill - Sasivekalu Ganesha, Kadalekalu Ganesh - Virupaksha Temple - Hampi Bazaar
Group 2: Achyutaraya Temple - Courtesan's Street - Kodanda Rama Temple - Chakratheertha (Riverside Trek) - Sugreeva's Cave
Group 3: Purandara Mantapa - Ruined Bridge - King's Balance - Vittal Temple - Vittala Bazaar
Group 4: Laxminarasimha- Badavi Linga - Krishna Temple - Chandikeshwara - Uddana Veerabhadra Temple
Group 5: Lotus Mahal - Watch Tower - Elephant Stable - Guards Quarters - Underground temple
Group 6: Queens Bath - Mahanavami Dibba - Pushkarni - Secret Chamber - King Audience Hall - Hazara Rama Temple
Group 7:Bhima's Gate - Ganagitthi Jain Temple - Malyavanta Hill - Talari Ghata Gate
Group 8:Pattabhirama Temple - Archeology Museum.
Start the itinerary with Group 1. This is located very close to the Hampi bus station area.
Though you can explore Group 1 in any order, start from the slops of Hemakuta Hills. The main highlights of this hill are the two massive images of Ganesha. Furthe up in the hill are a large number or old temples.
Once the Hemakuta attractions are done, head to Virupaksha Temple. From there you can go ahead and explore the Hampi Bazaar, starting from Virupaksa Temple and Monolithic Bull pavillion at the far end of the Hampi Bazaar.
Once Group 1 is done you can either go for Group 2 or Group 4. So you'll need to decide based on you interest . Group 2 is essentially a trek along the riverside till Vittala Temple. If you are on a moped, you can not take it along in Group 2 route. Leave it at Hampi bus station area.
If you skip Group 2, continue with Group 4 after Group 1 which is accessible by road.
For Group 2 route, start from the Monolithic Bull (Nandi) at the far end of the Hampi Bazar area. A short trek across the Matunga Hill will bring you to the middle of the Courtesans' Street. On your right in the Achyutaraya's Temple. Once this temple is visited , trek along the Courtesans' street till the river side. You'll pass the Rangatha Temple with a beautiful reclining Vishnu image in it and the Varaha Temple .