an easier way to get the cores is to farm the Robot Masters themselves on the Robot Master stage below the Mecha Stage. The robots are randomized each time you enter the stage, so it's best you keep grinding them down until you get as much/many cores as you want. I hope this is helpful for you.

My preferred way is to go to Light Chapter 5 Battle 1. Enker is a Shield core machine and can summon Beaks. Furthermore, both units are weak to Impact and Explode, so I would advise using Astro Crush since it hits both units and KOs both units. However, if you're farming for specifically Laser cores, just stick to using 1-target moves since Enker sometimes spawns Beaks in, thus increasing the chances of getting a laser shard per battle(you can get more than 1).

@RoseBlackDXZ : I was talking about Shield and Laser Cores, There are no Robot masters that are Shield or Laser Cores. (Yet...)

@GammaGhost : Thanks! That really helped!