There are three things about Beheeyem that fit together that should pique your interest upon immediate inspection of this kooky alien. First, its gigantic base 125 Special Attack. Second, its incredibly low Speed. And third, its ability Analytic. When combined with an item like Life Orb, Beheeyem's damage output is near-insanity. To make the most out of this power and its stat spread, Beheeyem will almost always employ an offensive Trick Room sweeper set, which flips the tables on a huge portion of RU teams and lets Beheeyem sweep quite handily. Beheeyem will also sometimes be seen simply wielding a Choice Specs to make the absolute most of its power. Outside of these roles though, Beheeyem is totally outclassed by the multitude of other Psychic-types that reside in RU, particularly Uxie, Mesprit, Sigilyph, and to a lesser extent Gardevoir.
The idea with this set is simple: get Beheeyem in late-game, set up Trick Room, and proceed to destroy all that stand before you. Beheeyem has a lot of options at its disposal, but it can only have so many on its set at a time, so your team needs to patch up the holes that Beheeyem will miss in its coverage. Psychic is the main STAB option since it blasts through many of the more physically defensive-inclined Pokemon in RU, particularly Tangrowth, Amoonguss, Crustle, Rhydon, and Feraligatr. Psyshock is also viable and hits Cryogonal, Clefable, Gallade, Hitmonchan, Hitmonlee, and Lilligant significantly harder. Thunderbolt gets fantastic coverage when paired with Psychic-type STAB, nailing Mandibuzz, Slowking, and Crawdaunt for super effective damage and getting a nice hit on Drapion, Spiritomb, and Absol. In the last slot, Substitute is preferred to let Beheeyem dodge Sucker Punches and block status. However, Hidden Power Fighting is an option as well to blast Steelix and other Steel-types, as well as get a super effective hit on Absol.Team Options & Additional Comments >>>
Signal Beam is an option for a super effective hit on all of Absol, Crawdaunt, Tangrowth, Uxie, and Slowking in one move, but it's not as strong a hit on Drapion or Mandibuzz and other major threats such as Moltres, Omastar, and Sigilyph. In most cases, Psychic STAB + Thunderbolt grants Beheeyem the best possible coverage. Dark Pulse and Shadow Ball are other coverage options as well but are outclassed by Signal Beam and Hidden Power Fighting overall. One of the dual screens can be put in the last slot of the Trick Room sweeper and could possibly lengthen Beheeyem's sweep, but most of the time its better off simply firing off powerful hits.
Choice Specs + Analytic grants Beheeyem truly terrifying power, but it's so slow and relatively frail that it's hard to get in and fire off an attack successfully (granted, when it happens something is likely going down). A Calm Mind set could be used since Beheeyem is decently specially bulky, but its Speed and physical frailty is an issue when compared to other Calm Mind users like Uxie and Mesprit. The rest of Beheeyem's support movepool is simply used better by the other Psychic-types in the tier.
Checks and Counters
Spiritomb is the best initial counter to Beheeyem. It's immune to Psychic and Hidden Power Fighting, is neutral to Thunderbolt, takes advantage of Trick Room itself, and does a major number on Beheeyem with Shadow Sneak, Sucker Punch, and Dark Pulse. Drapion is another good answer as it too is neutral to Thunderbolt and immune to Psychic and annihilates Beheeyem with Crunch. Absol and other Dark-types can work but Hidden Power Fighting and Thunderbolt are major threats. Slowking is a great answer to Beheeyem despite the weakness to Thunderbolt and can status Beheeyem or 2HKO it with Scald after Stealth Rock and Life Orb damage.
Uxie and Mesprit are good checks to Beheeyem as they can stall out Trick Room turns and take little damage from Beheeyem's attacks. Steelix, Klinklang, Escavalier, and other Steel-types make good checks as well but should be wary of Beheeyem's coverage options. Sucker Punch, ExtremeSpeed Entei, and Aqua Jet Kabutops are great answers to Beheeyem under Trick Room if your team lacks any bulky check to it. There are actually a few options that can tank a hit from Beheeyem and OHKO back or status it such as Bouffalant, Druddigon, Lanturn, and Magneton. Finally, if Beheeyem is outside of Trick Room, don't beat around the bush, just hit it with whatever you got to weaken it.