Is there an automatic level adjustment for bosses?

I'm fairly early into the game, but while most mobs I encounter have a fixed level display, it seems like a few mobs change levels after several seconds in combat.

For example, the boss in the Amusement Park began the fight at level 16, only to drop down to 15 after I had been shooting her for a bit (I was around level 10 at the time). The air battle with the Goliah in the ruined city also started at level 20, only to drop to level 12 (nearly matching my level) shortly after the first few attacks.

Interestingly, I also came across a pack of Small Stubbys that started at level 12 and "upgraded" to level 14 when they engaged me (level 16-17 at the time?), though I have not yet encountered any other non-boss doing the same.

Since all of these adjustments happen in the first few seconds of combat, it seems like it might be an auto-difficulty adjustment. On the other hand, the game has no qualms about throwing quest mobs or overworld mobs at me a dozen levels higher than my level, so I'm not so sure.

Why are these enemies changing levels? Is it a specific trait for some machines?

I'm playing on Normal, if that makes a difference.

I'm not entirely sure what you're referring to here, as the only enemy that changes their level during combat is the first fight against Adam, where leveling up is his primary mechanic, and he learns moves and abilities as the fight progresses.

From my experience (over 100 hours of gameplay), there is no level adjustment at all with machine lifeforms. The only enemies whose levels scale with yours are the wild moose and boars, which is why they become the only real threat when you've maxed out your level. Regular enemies and bosses have set levels at different points in the game. This is especially apparent when you unlock Chapter Select and go to previous chapters (or even previous routes) and go through the areas again.

For instance, I went back to fight Beauvoir again (the amusement park boss you mentioned), my AI-controlled 9S killed her in a single hit and kept her down for several minutes, until I realized she needed to be up long enough to go back onto the stage to move the fight to the next stage, at which point, I had to turn his AI to passive.

If I remember correctly, enemies will never be higher than level 60-65, aside from the golden bunny statue and DLC arenas, where enemies have set levels that exceed 100 in some cases. Additionally, bosses (aside from the one case I mentioned) will never change levels.

I don't think difficulty level has anything to do with enemy level, either. I believe it just makes enemies more powerful without adjusting their level.