Sound or motion activated long term battery powered Arduino
What you want to do after the triggering is an important part of this design.

An Arduino platform is not necessarily the best choice for power sensitive applications.  You identified one problem in your post: Linear regulators.  What you are likely wanting is an efficient switching power supply to support a wide range of voltages as your batteries drain.

Many embedded processor have low power modes.  Some are specially designed to reduce current draw down into the nA range when idle or sleeping.  However, all such processors require special care when configuring for these deep sleep modes.  That is to say, the application plays an important roll in deciding how to put a processor into such modes.

Supporting hardware is perhaps the most important aspect of a low power designs.  Contributions from the most advanced low power processors can be wiped out if supporting hardware runs at mA ranges.  A simple 10K pull up resistor will draw 0.5mA in a 5 volt circuit. The impact is meaningless in a mains powered application.  But for long term battery operation is could means days of lost time.

All that said, there are resources for Arduino low power operation.  Here is a low power library.  You will have to decide if it is sufficient for you application. Or if you need to also investigate low power hardware solutions.