I've been researching this for a bit and can't seem to find anything in the API reference page (https://developer.paypal.com/webapps/developer/docs/api/#sale-transactions). They show how to pull a specific sale transaction, and how to refund a sale transaction, but there is no mention of being able to pull multiple sale transactions through date range parameters or something of the like.
Is this possible?
Currently, you can't pull a list of sale transactions directly. However, you can get a list of payments, which can be sorted/filtered and do contain child sale transactions: https://developer.paypal.com/webapps/developer/docs/api/#list-payment-resources
seems, you need Paypal NVP API https://developer.paypal.com/docs/classic/api/merchant/TransactionSearch_API_Operation_NVP/ As I understand, Paypal REST API doesn't support this kind of operations