Are the Batch jobs running BULK inserts for example? If so, then for the period of the batch job running you could place the affected database into the Bulk-Logged Recovery Model which would reduce the size of the transaction logs considerably before changing back into Full. If you decide to use this technique however, you would need to be sure to perform a Full backup after the batch has finished to ensure you have a platform for your next transaction log backup.

You could also perhaps consider (but only consider!) whether or not you need to run the database in the Full Recovery Model. Obviously, if point-in-time recovery is important with regards to this database then the only option wold be full. If however, a combination of Full and Differential backup would suffice, you could save an enormous amount of a) space for the transaction log and b) time taken to complete the backup.

The move out of the Full Recovery Model should not be taken lightly however and testing the scenario in a safe environment would be highly recommended!