ok please post the EVs instead of the stats. it makes it hard to read, and makes this team look a little unprofessional
Tyranitar's nature should be adamant or jolly, not relaxed as its moveset isn't defensive nor is it a pokemon meant to be a wall.
There isnt much reason to have both rock slide AND stone edge on tyranitar. Id just take rock slide to hit both opponents. Replace stone edge with crunch.
Fire fang is meh, because the only pokemon it really hits harder than any of your other moves is levitating bronzong and skarmory, both who you really cannot touch anyways.
Id replace it with taunt (to really annoy set up teams such as trick room) or protect, a very useful doubles move
Flygon is a hacked pokemon. There is no way it can be naughty and have 328 speed, as naughty increases attack and decreases special defense. If you meant naive then that would make much more sense, as some people get uncommon natures confused.
Draco meteor is fine, but make sure to pump some special attack EVs into it so it can deal a good amount of damage. fly is just a no no, sorry to say. Replace it with Dragon claw.
Same with dig, it just is a terrible move. plus, when you dig, you can be hit by EQ from tyranitar, so that isnt good either. Id say replace it with EQ or fire blast (since this team has IMMENSE trouble with skarmory and bronzong). If you go EQ, go with protect on tyranitar to avoid damage.
Hyper beam, hyper beam, hyper beam... tsk tsk tsk, a big bad move. NEVER use hyper beam ever. Id say that stone edge/fire blast/EQ can fill the slot, depending on what you chose for slot 3. You can even use tailwind to give your team some speed!
Shuckle looks fine, but please post its EVs... if you ever use this on random wifi where OHKO moves are common, you may want to change your ability to sturdy, since gluttony is completely useless since you are holding leftovers
Id replace aggron with a heatran to combat bronzong and skarmory since the only pokemon packing a super effective move to them is flygon's fire blast and registeel's zap cannon (which only hits skarm for super effective, not zong and has shaky accuracy). Oh, and meta's t-punch. You can make a set and post it since im not feeling the need to make one for you. Just dont choice it because those aren't always the best items in double battles.
Metagross looks fine I guess, but Id really like to put explosion somewhere in there. The only place i would think is t-punch, but since you have trouble with bulky waters and skarmory, i wouldnt recommend changing it.
Registeel has no reason to use shadow claw, really. I like zap cannon! its innacurate, but replaces t-wave for a good damaging move that also paralyzes. I also like toxic, since it can help wear down bulky waters. Just be careful to toxic first and then zap cannon, so if you miss they wont switch, and so they wont get paralyzed in the process if you hit.
Id say explosion over shadow claw, since all your pokemon resist it, and some have protect. Just make sure to give it some attack EVs and you're set
EDIT: i just noticed that this isnt doubles :/ haha so if I mentioned anything about it (like explosion also hitting your pokemon) just ignore it