The usual cause of this issue is caused by third party software, such as the DS4 program. Helldivers supports most controllers, so you should not need any additional programs - try disabling it.
If you are using a third party gamepad, check to see if Steam has recognised your controller and already loaded in a default profile. When launching Helldivers, sometimes Steam can pick up both inputs, one from your gamepad and one from the automatic default profile, resulting in double input. All you need to do is disable Steam controller support in Big Picture Mode.
To get your DualShock 4 set up on Steam, launch the Steam client and click the controller icon at the top right to enter Big Picture Mode, which is Steam's console-like, controller-friendly interface. From there, go to Settings > Controller Settings and make sure "PS4 Configuration Support" is toggled on.