I don't think shooting would be the least energetic. I shoot competition air rifle myself and it's extremely difficult. You have to be able to contract certain muscles at certain times in different positions. It takes skill to do it and most people think all we do is just stay still the entire time. It may look like that to an outside person but when you're in our shoes it's completely difficult. Shooting is a very misunderstood sport. As for archery, it's extremely difficult as well. I've spent a while shooting archery myself but found it wasn't my cup of tea. It's similar to shooting but very different at well. In both sports you are trying to be as still as possible while lining up your shot with the center of the target. In shooting you are contracting your muscles for long periods of time but not quite as much as you need to in archery. In archery you are contracting muscles a lot more but for shorter periods of time. I personally believe that archery is the least energetic because not as much effort is put into the entire competition as in shooting.

If you are looking at energy in terms of calories burned, then the answer should be shooting, where in order to hit a target successfully you have to be able to keep still. Archery, while physically more demanding, still doesn't involve much movement so would burn fewer calories than more active sports. Of these, probably cycling is the most energetic in terms of calories burned; but that doesn't need to mean that it is the most difficult or demanding of all. In fact, if you think of the effort involved in qualifying for the Olympics, it would be hard to describe any event as the least energetic.

However, this certainly doesn't mean that either shooting or archery are less demanding than other sports. For one thing, to develop the concentration and precision that you need, you have to be in excellent physical shape; for another, participants in these events do use enormous amounts of energy in planning, concentrating etc.

There was a debate about this some years ago, which is still relevant today; you can find it here.