For the Circuit Breaker and Security Expert achievements, is it a matter of completing the hack within a certain time limit? If so, how does one know what the time limit is?
It is based on time. The time starts ticking when you make your first move, at least it does for the lockpick challenge. You can gauge roughly how much time remains using the meter at the top, "Actuator Charge". The time available varies based on the complexity of the challenge (e.g. number of rows) and the difficulty chosen, but it isn't very long: often less than ten seconds.