Logic of a flying enemy

I want to make a 2d flying enemy. If you look at some popular game that has flying enemy like dead cells, rogue legacy,etc you can see there are a lot of ways to move the enemy (parabol, bezier curve, sin, cos function,...). So what is a general way of moving it or each game has a uniqe approach to this? And how to do that?

 

There's no general way. Each movement type has its unique "mover" or "move algorithm" and that's it. That's the simplest approach.
You could try to generalize paths as splines, but this is not necessarily worth it.

 

Surely the movement path of an enemy is part of why you introduce that enemy in the first place? Enemies are active obstacles, so their movement and attack patterns inform, and feed back from, how you want to player to have to react to 'beat them'.

 

For examples, how to make an enemy move like the "bat" in dead cells.

 

Generate some sort of navigation graph in XY plane (i think i even saw some1 do this with unitys navmesh) then use A* or similar to solve path. I've used this style of approach for flying enemies or top down 2d pathfinding.