The storm troopers were ordered not to hit the rebels, because Grand Moff Tarkin hid a tracker on the Millennium Falcon and wanted to track the rebels to the rebel base. Can't track them if they're dead. There are multiple lines of dialogue in the film explaining this.

If the Star Wars RPG, Stormtroopers are brutal and you pretty much avoid them like you would an overpowered boss battle. Same with the novels I think

It's that impenetrable plot shield those rebel scum are using.