Kabutops thrive in this offensive RU meta. There are hard-counters to Kabutops like Tangrowth, Poliwrath, and Quagsire, but you hardly see them (or pure stall in general). After Swords Dance, Kabutops just wrecks.
Standard Kabutops
Kabutops @ Life Orb
Trait: Weak Armor
EVs: 252 Atk / 252 Spe
Adamant or Jolly
~ Stone Edge
~ Swords Dance
~ Aqua Jet
~ Rapid Spin / Waterfall
Although august said its hard to set up Swords Dance, I personally find many opportunities for Kabutops to set up, whether it be on Entei locked into a wrong move or Archeops / Moltres fleeing for its life. Such scenarios are easy to replicate.
Rapid Spin is dispensable. We like to emphasize Kabutops's spinning capabilities, but Kabutops as a Pokemon is really better off with a more offensive choice. And it's not like using Kabutops for anything else other than spinning is a waste of a poke-slot - with a powerful Aqua Jet for sniping down faster threats and sweeping after a SD, it's very much like a Scizor of RU. There are MANY times where I had a choice to spin after the SR lead is dead, but I decide to just go 100% aggro and end up taking out half of the team with Kabutops.
For this reason Moltres is not the best teammate for Kabutops (although Kabutops is an amazing teammate for Moltres), because it necessitates Kabutops to waste a slot in Rapid Spin. Plus Moltres really doesn't help with Kabutops weakness to Grass-types (as most of them sport HP Rock), and only compounds the team's weakness to electric-types.
Good Partners for Kabutops
Escavalier by august - it serves as a reliable Lilligant counter, and also not a shabby Sceptile check either (w/o HP Fire). CB Megahorn is nice for defensive Grass-types, too.
Unlike Moltres, Entei is not deathly weak to SR and have some nice bulk to it. Even more it has a powerful CB ESpeed to check stuff that Kabutops cannot with Aqua Jet, providing some nice priority core. CB Flare Blitz from Entei, just like Megahorn from Escavalier hits hard, especially against Grass- and Steel- types that resists Kabutops' Stone Edge, and is really hard to take.
Druddigon is probably one of the most solid offensive checks to Grass-types. It also doubles up as a decent check against Electric-types, too. With its insanely powerful LO Outrage complemented with Sheer Force-boosted Fire Punch, it can literally punch holes against the opposing teams even if they have a dedicated physical wall. Druddigon is definitely a good wallbreaking choice to pave a sweep for Kabutops.
You can't go wrong with Nidoqueen on an RU team, but it does provide some tangible benefits to Kabutops. The absorption of Toxic Spikes is REALLY helpful in keeping Kabutops around for its grand performance. Nidoqueen also likes to attract mons that are set-up bait for Kabutops, such as Cryogonal or Moltres. Nidoqueen also has enough bulk to tank a powerful STAB Grass move in exchange for a Sludge Wave KO, allowing Kabutops to spam Aqua Jet without worries.
Obligatory mention of Gothitelle, since it can remove at least 1 physical wall that counters Kabutops should the opponent use one. HP Fire eliminates Ferroseed, while Psychic should easily dispatch Tangrowth, physically-defensive Amoonguss, and Poliwrath. Energy Ball can be used for Quagsire.
LO and SD is indispensable imo. Aqua Jet wont be anywhere near as awesome otherwise, missing on some cool KOs like a +2 LO Aqua Jet OHKO on Galvantula.
Rain Kabutops
Kabutops @ Life Orb
Trait: Swift Swim
EVs: 252 Atk / 252 Spe
Jolly or Adamant
~ Waterfall
~ Swords Dance
~ Aqua Jet
~ Stone Edge / Superpower
This is Kabutops' best set. Kabutops' measly 80 base Spe and reliance on 40 BP priority and Stone Shit are its main shortcomings. Give it Rain, and now it's the fastest mon in RU (ok there's Swift Swim Qwilfish and Floatzel, but w/e), with a 120 BP 100% accurate Waterfall. Seriously, just mash the Waterfall button to victory - very few teams are prepared for this, because of the current offensive nature of RU.
Stone Edge is of course a given since it provides some nice coverage and STAB, but if you're tired of Stone Edge being one of the shittiest move in the game, then Superpower is definitely a good alternative. The move is especially useful to Rain teams, since Ferroseed is one of the toughest mon to face, and it's nice to easily remove it without much hassle.
Awesome Rain Inducers
EonX mentioned a few of these - namely Uxie and Electrode. Uxie is great for providing Stealth Rock and bulk & Speed to guarantee that Rain goes up. Some like to give it Memento for a free switch-in to their Swift Swimmer, but Yawn + U-turn works, just as effectively. Electrode has access to the fastest Taunt in the game iirc, preventing any sort of set-up as it sets up Rain, maybe throw some Thunders, and Explode.
Lanturn is great on these teams, blocking Volt Switches and taking abuse for the team like Uxie. It also has a slow Volt Switch which allows it to bring in Kabutops & co safely. Special mention for Volbeat, whose Prankster puts up Rain virtually without fail, and whose Encore & Sub Pass easily providing safe entry to Kabutops and maybe even a Substitute to start setting up SDs.