The iconographical context of this combination is at the best sketchy. However the individual symbols are a lot easy to comprehended in an insignia . Vijayanagara kings were known for their (Hindu) religious patronage, and it is mostly likely that their emblems too reflects their affiliations.
The most unusual for an ancient Indian emblem is the image of a boar, though it is a significant symbol in Hindu Mythology. The third avatar (incarnation) of Vishnu is in the form of a boar (Varaha) . Boar brings the earth up from the bottom of the ocean. Essentially Varaha is a Vaishnava icon.
Just above the head of the boar the moon image in the form of a crescent. Probably the only place a present can be found in Hindu iconography is on the matted hair of Lord Shiva. In this context Shiva is often called Chandrasekhara, the one with moon as crest. However crescent as a standalone image is rarely found in Hindu iconography.
Sun god is worshiped as Surya in Hinduism. Suriya ( āditya ) is one of the ancient deity of Hindu pantheon right from the right from the Vedic age (1500 BC).
Lord Rama is considered as a descendant of the Surya (Surya Vansha). It is interesting to note the fact that the mythical layer of Hampi has some strong association with Ramayana.
The dragger portrayed in a vertical position, could be more of a royal icon than a religious symbol.
In any case a large number of structures commissioned under the royal patronage possess the Vijayanagara emblem on it. You can see them on the base molding of pavilions, gateways and even in Vijayanagara era coinage.
Apart from Hampi, you can spot the Vijayanagara insignia anywhere from Kancheepuram to Tirupati to Srikalahasti.