A few ways.
1) If the backup is ADSM server scheduled, a Q EVENT F=D will tell start and
finish time (why isn't this available via the
SQL interface %*&*%*)
2) If the client is V3, you can do a Q ACTLOG OR=CLIENT NODE=nodename
3) Check the accounting file records if your ADSM server has accounting enabled
4) Check the clients DSMSCHED.LOG