To acquire the Laser and Shield-cored abilities, you have to acquire and sell the cores of robots of that type to Reggae. For Shield, you can find these by fighting Enker, who either by defeating with a super-effective ability or by using 'Copy Soul' will usually yield a Shield-core.
Laser cores are a little trickier. There are no Robot Masters currently in the game who are Laser-core, so you'll have to fight the Beak. They're Mechas so using super-effective abilities will only make them drop shards, which'll take 4 pieces to make into a core. That's why I specifically recommend using Copy Soul on them as it'll save you much much much more time; using this ability will immediately give you a full Laser core.
Once you've sold around 10 of these cores to Reggae, he will create the Laser and Shield abilities and make them available for purchase.
If it turns out some players still have more abilities than you even after buying this abilities, don't fret. A lot of the older accounts often have abilities that aren't usable anymore and have been removed entirely from the game, but as a bug are still included in the total count of abilities a player has on their profile.

Long Story Short, Grind in Final Destination I in Dr. Light's Path