Question: As I understand it, mic level input and line level input are two different things, with line level input having a much higher power level.

In my case, I'm dealing with an old minidisc recorder that only has a line level input on it. This is using a regular 3.5mm jack.

I see plenty of attenuators/converters around for going from Line -> Mic, but what I am not finding is the reverse - an amplifier that would boost the mic level to line level, and simultaneously be portable for field recording.

*This is not a product recommendation post*, I just need to know if the thing I'm looking for even exists, is reasonable, and if a "3.5mm mic amp" is the right terminology for it.

Answer: 
Most microphones output about 0.0006 volts while line level is about 1 volt or 1.23

The device you want is a microphone preamp to bring the microphone signal up to Line level. If you get one with 1/4" out then it's not hard to go from 1/4 to 3.5mm. But I don't know of a battery powered one. You might need to buy a new recorder that has a mic input.
Yes, you can buy or easily make a battery powered preamp to insert in between a mic and the Line In input. I made one many years ago to do exactly this - total cost was about £3