This is one instance where you probably want to keep your feathers for healing instead of augmenting for damage; Bysurge's health pool is so huge it doesn't even help.
It isn't immediately apparent, but his normal swipe attacks don't need to be dodged every time. In a lot of cases, you can jump over or run past his normal swipe attacks without wasting the stamina. You want to keep your stamina up for his massive attack, which comes after he yells, "I need more energy!"
The biggest thing to keep in mind here is to avoid the skeleton/robot grabs, as they are going to result in immediate death. If your choice is to take damage from Bysurge or get grabbed, take the damage instead.
This might get patched out, but there's a small, recessed area to the far left where you can be knocked bock while blocking an attack with your shield. Bysurge can't hit you while you stand there with his normal attacks. The skeletons also can't grab you there! Hit him with ranged and heal when necessary when he uses his electricity attack.