In order to upgrade CISCO ASDM software we need to follow the following steps:

1.Download the software from Cisco Website (you need a cisco username)
2.Load the software to the device (ASA)
3.Cofigure the ASA (device to use the new version image file)

Step 1:
Downkload link:

Step 2:
To load the new version we use the ASDM manger with the following 3 options:
Tools -> Upgrade software from Local computer
Tools -> File Management
Tools -> Upgrade Software from

We can also upload the software using a TFTP server and the copy tftp flash command:
firewall#copy tftp flash

Step 3:
Once image uploaded to the Firewall we need to configure the ASA to point to the new ASDM software and use it (there is no need to reboot router after configuration)

To configure ASA to use new ASDM version:

In ASDM go to:
Device Management – > System Image\configuration -> Boot Image/configuration
Int the ASDM file path click browse and select the new ASDM image.

You can also change the ASDM boot image from the CLI command line using the following command:

firewall(config)#asdm image flash:asdm-613.bin

Step 4:
Save config, close ASDM and go to router page https://ip_address and start the ASDM.