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.
Are you sure about that line level input? The portable minidisc recorders (rather than mere players) I am familiar with have a 3.5mm input suitable for electret condenser microphones with plugin power. There are actual stereo lapel microphones for those recorders that were popular for bootleg recordings in olden times. Now that may not help a lot depending on which kind of microphone you are actually planning to use.

Note that in a pinch, an old USB audio interface with mic inputs/phantom power and failing driver support will tend to serve as a cheap stereo mic preamp that can be powered from a number of USB-style power supplies (including car battery use). They also make for reasonable headphone/line amps fed by the balanced return connections of a stagebox.