Hello ankurjandial, You can upgrade directly to Version F10_3_20e, A28 from your current version.  It is best to upgrade your library first then to upgrade your tape drive.  Also, make sure that you stop your backup software services before you start your firmware upgrade. Please let us know if you have any other questions.
Hello Support I have a Dell TL2000 library and 2xLTO6 tape drive and I would like to know which current firmware is available for my device and what is best path to upgrade to latest firmware. Is that i need to apply specific versions first before proceeding with latest one as there are few versions already available? Here is what I am currently running. Currently Installed Library Firmware C.00 / 3.20eBootcode Firmware Revision 0.80Drive: ULT3580-HH6  firmware: D2DBI believe the current library firmware is F10_3_20e but I am not sure whether can be directly upgrade to this version or need to upgrade to any other firmware first and same goes for Drives also? When you download the latest firmware, it provides you with all the firmware for all drives.
Dell PowerVault TL2000 Tape Library - Firmware Upgrade