I don't think you need Garchomp to win, Noivern is really useful with its high Speed and Tailwind, you might actually be able to do it with your current team. But I think you should optimize your abilities and natures first, just the improving of stats can really help after all, especially proper EV distribution.
Primarina is really slow, so Timid won't help much, better boost SpAtt or SpDef (Modest/Calm). And Liquid Voice without a voice move is useless, I would change it to Torrent or teach it Hyper Voice. How helpful is Aqua Jet to you? Primarina's base Att stat is low, so it probably does little damage. If you think you can replace it, then Icy Wind can prove very useful with its speed reduction. Or Reflect/Light Screen for team support.
Calm on a physical Lucario is hindering you, better give it a Speed boosting nature. Usually that'd be Jolly, but if you wanna keep Aura Sphere go with Hasty or Naive.
For Arcanine, Flash Fire is very situational and only boosts your Fire move. Justified would generally boost all physical moves so it might be better, but I'd go with Intimidate. It's always very useful against any physical attacker, especially against Titania who has 4 physical mons.
Cincinno looks perfect, Ampharos is also ok, although you could replace Power Gem or Signal Beam with a status move like Light Screen or Cotton Guard.
Lax for Noivern isn't helping it, better go for Modest. And before important battles, you might wanna replace Fly with a special move like Flamethrower, or teach it Tailwind as another team support move.