How can I make a partial refund on a customer's payment?

Navigate your way to the customer's profile page you would like to make the partial refund to, and click refund:

You can now edit the amount. Just type the desired amount, and then click anywhere outside this box to update the refund total:

Note. The refund total will be inclusive of any tax/fees.

You will also have the option to send a receipt to the customer, and decide whether to refund via original payment processor or offline/cash when not supported
or
apply as an account credit towards future purchases.

Once completed, click 'Process Refund'. Payment history will now show the partial refund:

NB. Only a subset of payment processors support partial refunds. Most only support refunding all of a payment, in which case a partial refund will be initiated via cash.