I have upgraded many PIX and ASA units using the CLI, However, I really like the upgrade feature in the ASDM software. But, I found that one has to take a few extra steps to ensure a successful upgrade when performing these actions on an HA (Failover) Pair, just like when using the CLI method.
During my last upgrade I documented the steps so that I could save it for future use, and thought this could be useful to others as well.
This upgrade was performed on an HA (Failover) pair of ASA 5515-X Firewalls.
Attached you will find a PDF that explains the procedure to perform the upgrade using the ASDM software.