A camera hidden inside the barn by members of Animal Defenders International (ADI) recorded Anne's treatment between January 21 and February 15 last year.
The court heard the secret footage showed Anne's keepers kicking, punching and even hitting her with a pitchfork.
In one recording from January 22 shown to the court, Mr Roberts can be seen entering the barn before landing a single kick on Anne's trunk.
Miss Law said: "The footage shows that the elephant was constantly chained by two legs for the entirety of the visible footage we have available.
"It also shows her being repeatedly kicked and hit by one of the defendants' employees with various implements including a pitchfork.
"Bobby Roberts was quite happy to legitimise the use of casual violence on this elephant."
The court was shown a clip in which Roberts could be seen to enter the barn before kicking Anne in the trunk while her keeper - known as a 'groom' - stands just yards away.
A series of clips was then shown in which the same keeper could be seen hitting and kicking Anne.
Miss Law said: "One clip which is quite illuminating about how these staff were taught to look after these animals and that is the clip of the footage which shows Bobby Roberts kicking the elephant's trunk in front of the same staff member.
"Here you have the member of staff, who Bobby Roberts says he adequately trained, seeing Mr Roberts kick the elephant and then doing the same thing himself 14 days later.
"Much of the violence took place in front of other staff members, that suggests a problem that is endemic and that the staff weren't concerned being seen using violence on the animals."
As well as failing to protect the elephant from violence, the couple are also charged with causing it unnecessary suffering by allowing it to be chained at all times.
The court heard that ADI made the footage public on 26 March last year, and it was quickly followed up by the police and RSPCA.
The pair faced three charges of causing unnecessary suffering to Anne under the Animal Welfare Act 2006.
They stood accused of chaining her to the floor, failing to prevent her groom from beating her and failing to ensure her needs were met.
Both Bobby and Moira Roberts deny all charges.
Moira Roberts denied ownership of Anne, meaning she cannot be held responsible for her welfare.
The magistrates court case was held at Northampton Crown Court due to venue requirements.
Proceedings were held in front of District Judge David Chinery and no jury was present.