This is one stage Rubhen and I were having a lot of issues with in co-op and came with a pretty good strategy.
Instead of running down the tower and shooting each and every lightning alter along the way it's possible to shoot most (possibly all) of them safely from the top floor. Shooting these will not start the fight and makes it extremely easy to focus on defeating enemies along the way.
While not completely confirmed, we found destroying the root at the bottom, which actually starts the fight, seemingly made things more difficult. This could be due to the increased amount of time spent at the start, or from a perceived increase in enemies. Either or, I wouldn't advise doing that.
At the bottom you just need to stay alive and you should get this done with relatively few issues.