A screenshot of you base when entering the second phase would help in giving advise as I am currently unable to give much more hints than already in this thread. For sure I know it's beatable, and since you now know there's a second wave, you might be able to prepare for that a bit better.
From what I remember, the runners spawned are much stronger if there are many runners, but their spawn rate is decreased (so killing more runners means more weaker runners spawn). Also, don't go after all corners at once, but take them one by one (going right and then up or down looks easiest to me). Taking them out really takes them out completely, no surprises after that, so you might want to rush one.
Anyways, that second wave is below my own quality standard