I've found a blast or two with a Fatty will take down the shields, followed up with an EMP grenade to kill the tank. If I know there might be one of those tanks on a mission I'll always bring 2 gals with fatties just for hovertank duty.
I try to avoid them if I can before I have that stuff. Blue shields take 25% from concussive, which is why your mortars didn't scratch them. They also take 25% from piercing, so regular guns are out. Laser, plasma, electricity, cut, and stab do 100%, so an intrepid melee girl or two might bring it down. It's no picnic once the shield is down, though. They're resistant to varying degrees to most damage types, even melee types. They take bonus damage from EMP and even more from warp. Your best bet if you don't have either is piercing, which they take 80% from. But even then it's a minimum of 90 armor everywhere, and higher on the sides and front. 37mm rifles have a chance, and recoilless rifles, but they're a tough nut to crack without EMP