Finally managed to bring down a Bouncer Big Daddy without dying. Only one medkit, too. Basically, it takes 8 rounds of electrobuck and some armor piercing pistol ammo. You have to shoot him while he's charging at you - his weak spot is on top of his head. If he's too close and won't charge, electrobolt him and run. Same if you need to reload. Still not easy though...
The Eve Capacity upgrade coupled with the Eve Link tonic has been a great combination. All I need to buy is medkits ($15/ea at a hacked machine) and I often have more Eve than I can use.