im not saying bad el can 100% solo him, its a theory, but he would 100% have to be wearing a regen set if he did, with very high hp/def/speed , with a blood ring, i think he has a chance.
this is the method i use for my orn, but the difference with orn is he has a psn on his a1, so even if i get stuck into a provoke cycle orn will keep psning him with a1, but if bad el had blood ring he should be occasionally able to break the cycle of provoke and land psn, and with the healing from regen set / and his a1 he should be able to survive solo assumiung he has enough hp/def.
if u dont have a bloodring, you could try taking another champion that can also do a similar thing in a regen set such as UDK who can apply some extra shield and absorb some hits while bad el is doing his thing, and run it as a 2 man(or at least make sure the others die off before boss fight or very early into it), because if even one of ur team falls into that provoke cycle vs him it can bring the other usually unkillable champions down with them because they are taking far more hits than usual.-
thoughts on Gnishak? (Do you have him) he has bombs on A1 and A3... the bombs convert to protected poisons...