Upgrade BIG-IP version from BIG-IP 10.2.1 (Big-IP LTM 1600 hardware) to BIG-IP 10.2.4 Build 591.0 Hotfix HF2

ouch.. long time I haven't seen a 10.x version. I'll try

Upload the software and hotfix to the BIGIP (System / Software). Select the Software and "Install". Select a volume where you want to install it (either an existing volume which is not the active one or you can type a name of a new volume). After SW is installed, perform the same (selecting the same new volume!) for the Hotfix. Then you'll go in the System / Software / Boot and select the new volume to boot. That will reboot the BIGIP, perform post-install operations (install the actual config) and that should be.