How do I contest a false charge back claim as a merchant?

TLDR at the end. 

My dad owns a local goods business in the city, and is facing a chargeback claim against one particular transaction. A lady customer who visited had a failed transaction attempt (she claimed her money was deducted, my dad said it would be refunded), in the second attempt the transaction succeeded. However the next day this lady returned saying her amount wasn’t refunded and that she needed money for her daily expenses, my dad denied. 

Now this lady has gone ahead and claimed a chargeback against this. (My dad remembered this particular transaction and had taken photos of the failed transaction to show to her). Recently he received a call and email from his bank saying one of the customers has raised a chargeback request against a transaction under the reason Goods/services not provided. It asks for proof such as transaction slip, signed invoice and explanation letter. 

We do have the transaction slip from the card machine, a generic invoice without customer signature and a letter which I will draft defending it(it's a small local shop and no one ever takes signatures on invoice here). However I’m not sure how exactly the bank can prove who is correct since the matter will just be a he said-she said. I’m sure she won't have any proof of goods not provided either. At best I will just explain how the lady came back to claim a duplicate transaction the next day and show the failed transaction as proof of this. 

It would be really helpful if anybody can provide any inputs as to how to tackle this situation? Also what steps can a merchant take to avoid such situations in the future. I’m thinking of stopping credit card transactions altogether to avoid this.

Thanks in advance.

TLDR: My dad’s business received a chargeback claim against a transaction claiming goods weren’t rendered even though goods were rendered. Bank is asking for proof of this.