Hello Andrew, I have always upgraded BIOS/System Firmware, RLM Firmware,Disk shelf firmware and disk firmware separately before doing the ONTAP upgrade. It is important to know that BIOS/System Firmware, RLM Firmware and Disk shelf firmware require a system reboot. Thus, its absolutely important to check and perform a cluster failover to test if the cluster failover works. RLM firmware can be done outside the cut over window, because rebooting the RLM wont impact the actual controller and can be done via out of band mgmt.Disk firmware update is non disruptive and can be performed while controller is in production.
Prior to ONTAP Upgrade, Check for SnapMirror compatibility if you are using snapmirror. Both Source and destination are expected to be at a required ONTAP level for Snapmirrors to work.
Also backup ifconfig-a, etc/rc and etc/hosts files before you start with any of the upgrades.
Prepare as much as you can, and if you use CIFS try to upload all the required software downloads to /etc/software directory. That will save you a lot of time. I use the RLM to do the upgrades or use the serial port, to avoid any SSH or network timeouts.