> I am searching for a battery preamplifier schematic optimized for Shure SM57 (or other dynamic microphones) I need this preamp for "on the fly" recording
There is SO much you are not telling us. You will continue to get random suggestions until you tell better.
What are you going into? A radio network? Presto disk-lathe or a mike input on a pocket recorder, or a line input, or? ? ?
How much gain do you really need? If you are going to a mike input, you don't need much gain at all.
How close is the SM57 to this preamp, and how adverse is the environment? If the SM57 is within a few feet of the preamp you do not need balance input; if hundreds of feet of cable anywhere around utility power, you need careful balancing.
This has been built several times, it works, is clean up to reasonable limits. It was "noise free" in a large practice room with lots of fluorescent lights, usually some blower rumble, and 50 foot unbalanced medium-Z mike lines.