Here is my short instruction to perform Cisco ASA firmware upgrade with zero downtime.

Backup and Download

Fist we need to backup configuration and loads new firmware/ASDM(Device Manager) to ASA devices.

Primary ASA Firewall

Backup current configuration on fw-primary.

fw-primary# copy running-config flash:/backup-config.txt

Backup configuration to your computer via TFTP.

fw-primary# copy flash:/backup-config.txt tftp://10.10.10.15

Download firmware image file from your computer via TFTP to fw-primary.

fw-primary# copy tftp://10.10.10.15/asa903-k8.bin flash:/

Verify integrity of firmware image file.

fw-primary# verify /md5 flash:/asa903-k8.bin

Download ASDM image file from your computer via TFTP to fw-primary.

fw-primary# copy tftp://10.10.10.15/asdm-722.bin flash:/

Verify integrity of ADSM image file.

fw-primary# verify /md5 flash:/asdm-722.bin

Secondary ASA Firewall

Backup current configuration on fw-secondary.

fw-secondary# copy running-config flash:/backup-config.txt

Backup configuration to your computer via TFTP.

fw-secondary# copy flash:/backup-config.txt tftp://10.10.10.15

Download firmware image file from your computer via TFTP to fw-secondary.

fw-secondary# copy tftp://10.10.10.15/asa903-k8.bin flash:/

Verify integrity of firmware image file.

fw-secondary# verify /md5 flash:/asa903-k8.bin

Download ASDM image file from your computer via TFTP to fw-secondary.

fw-secondary# copy tftp://10.10.10.15/asdm-722.bin flash:/

Verify integrity of ADSM image file.

fw-secondary# verify /md5 flash:/asdm-722.bin

Firmware Upgrade and Failover.

Both of my Cisco ASA firewall are already configured to Active/Standby Failover

Specify the system image that the ASA loads at startup

fw-primary# conf t
fw-primary(config)# boot system flash:asa903-k8.bin
fw-primary(config)# asdm image flash:asdm-722.bin
fw-primary(config)# wr
fw-primary(config)# sh running-config | i boot
fw-primary# sh asdm image

Make sure that fw-primary is active then reload fw-secondary(standby) to boot a new firmware image and ASDM image.

fw-primary# sh failover state
fw-primary# failover reload-standby

Configure fw-secondary to active  and reload fw-primary(standby) to boot a new firmware image and ASDM image.

fw-secondary# failover active
fw-secondary# sh failover state
fw-secondary# failover reload-standby

Configure fw-primary back to active as it should be.

fw-primary# failover active
fw-primary# sh failover state