I could sit and speculate all day and you wouldn't be any further than you are now. See if you can enlarge that wallet-size discharge and send me a scan of it. Maybe I can make out enough to get you pointed in the right direction.
The bronze arrowhead device denotes participation in an amphibious or airborne assault. Only one such device is authorized to be worn with any one service/suspension ribbon so he may well have taken part in more than one assault. All named campaigns and assaults should be listed on his discharge but space was limited. The only other way to determine which and/or how many would be to access records.