Lugia checks a ton of stuff, albeit it is setup bait for a ton of stuff too (probably your reasoning for your bias against it, am I right?), but it gets Thunder Wave, Dragon Tail, Whirlwind, and Toxic to try to avert that so you can't blame it too much. In particular, it can phaze / Toxic Fighting, Ground, and Water Arceus.
Adding on to what Sand teams are weak too, Calm Mind Ground Arceus and Water Arceus can be a real pain. Ground Arceus tends to annoy teams not utilizing Palkia while Water Arceus flourishes on teams lacking a Latias. Both can stomp over Giratina-a if they use Ice Beam (which they often do).
Tyranitar can take advantage of the ubiquity of these (Lati@s) Pokemon and trap them with Pursuit or Crunch them to death giving an early 6-5.
Actually Tyranitar is screwed if it switches into Surf, Grass Knot, or if its running a set that lacks Special Attack investment, Calm Mind. Surf and Grass Knot 2HKO Tyranitar.
Going to mention this again, Furai referred to it earlier. Partners that can bait Ice Beam or Thunder from Choice Kyogre (see every Specs Kyogre switch-in in the game), work well with Tyranitar since Tyranitar can switch into the Thunder / Ice Beam and Pursuit the Kyogre which helps in winning the weather war. That or the Kyogre doesn't spam Thunder or Ice Beam which just helps your Specs Kyogre switch-in.
Mention Gliscor! Sand + Toxic poison residual damage is really devastating x_x, combine that with Taunt and you should be killing stuff pretty fast. It doesn't benefit much from sand aside that though :(.
Also ctrl + f Deoxys -> No results. Tyranitar is one of the few things that can stop Deoxys-S from setting up hazards. Deoxys-S is forced to either lay down 1 layer of hazards or Taunt to prevent Stealth Rock from coming up since Crunch brings it down to sash and Sand breaks sash.
Do mention that non-rock / Steel / Ground Arceus may get annoyed by constant 6.25% wittling away at their HP bar :P. Samething with Giratina-O and Chansey.