Their high health and armor may be intimidating but Krogan Prisoners don't take cover and lack regenerating shields. As such, simply firing high DPS M-96 Mattock Auto or the M-333 Particle Beam mixed with abilities like Salvo is the best way to take them down. However, like most of the krogans, their health bar will regen at a high rate.
Like with other humanoid enemies, their heads act as a weak spot, and shots landing there inflict bonus damage.
They can be equipped either with M-333 Particle Beams or M-22 Eviscerator shotguns. They will close in rapidly regardless of weapon used, and their Berserker charge does a lot of damage and will force you to get out of cover.
Because they are immune to Leash, using a biotic Pull is the best way to stop their charge.
Keep your distance from these adversaries and use your Tactical Cloak if they get too close to get away.