You will need the Limited Write Contributions permission to download a batch's reports. To open a batch someone else created, you also need Unrestricted Batches or Full Read Contributions, and the batch must be at a campus you have access to.
To locate the batch, go to Contributions > Batches in the left-hand menu. Click the name of the desired batch and go to the Actions menu in the top right. There are two reports to choose from. The report will automatically download when one is chosen.
Overview
This report will give summary information on the batch without showing the individual transactions. See below for an example of this report.
Transaction Details
This report contains a listing of all the transactions entered in the batch. See below for an example of this report.
Tip: Both reports cover every transaction in the batch, including gifts placed at campuses you cannot otherwise see on the Contributions list. A batch lists everything it holds once you can open it.