EAT is a bit high risk high reward with Bile Titans. Wait just before (or dodge) the puke shower and aim at the mouth. Other option is to shoot at their underbelly, but it seems to need more damage on top of two EATs.
We had two members with EATs basically littering them on our path whenever the cooldown was off. That way there usually is couple of EATs to be used when stuff hits the fan. You can also destroy the pod they land in, so the EATs show up in the map as well, which makes them easier to find when needed. Usually patrolling bugs will take care of the pod, though.
Yeah, basically I always try to aim at the mouth facing as directly as possible in front of them.