If you don’t know what beholders are (the basics) you should read up on the Wikipedia article for them or even better the post at Power Score about them. Suffice to say, beholders are alien things from another dimension/reality that are not only an iconic D&D monster from way, way back, but also the feature monster on the cover of the 5e Monster Manual. They’re a signature character, as much a part of D&D as anything at all can possibly be.
Playing or deploying beholders in combat, RP-ing them so they pop and stand out is hard. Playing, say, gnolls or hobgoblins I found easier–as a DM. There’s a logic there that’s primitive for one and pretty classical for the other. Playing orcs or goblins is harder, but its still tribal and makes a “behavior of tribes” sense. Dragons are tricky to get right because they’re so large (in stature, I mean) that unless you go very BIG with the performance, you’re really just playing a mean person in the body of a dragon.
Beholders and aberrations or intelligent monstrosities are hard because they are–entirely–not human, not primate, not terrestrial. They are an alien mind. The Monster Manual tries to reflect this by emphasizing paranoia and arrogance, but I like my beholders to go to truly scary levels of alien. The less predictable, the better. The more the party feels like they cannot reliably relate to whatever a beholder thinks and feels the terror of what they see as irrationality (but is simply an alien rationality) the better.
So, here are my tips for playing beholders: