I guess to stop the Great Devourer would be a real epic campaign. Besides that, I guess there are multiple szenarios to succeed against the Tyranids. Destroying a Genestealer Infestion as described in the Introduction adventure and even bringing down a Hive Ship. That said I guess it comes down to kill the big beast that the lesser Tyranids fall into disarray.
Furthermore, iirc, even the Tau have noticed the Tyranid threat and Commander Flamewing (Mark of the Xenos) is looking forward to work together with the Imperium to stop the advance of the Great Devourer. Maybe this would be chance to stop your ongoing campaign and switch to the Tyranids.
On the other hand, I guess as much as the Tyranids are terrifying they are interesting. Spontaneously I'd think about these szenarios:
The Kill Team answers to an emergancy call from a space ship and notices a Genestealer infestion. Although this encounter did not pose a threat (or maybe) to the Kill Team, they start to learn that the Genestealers seemed to be part of the cargo. Tracking its back the ship's origin they find a planet with a huge Tyranid Experimental Lab.
They must learn that this Planet / Lab is run (or protected) by an Inquisitor who starts to send infested ships throughout the sector to make the Imperial Guard and / or Planetary Defence Forces learn to fight the Tyranids. Think about an Radical Isstvan Inquisitor as described in the Radicals Handbook.
Alternatively the Lab can be run by an Mago Biologis who views the whole subsector as a huge experimental playground. At this point the Kill Team has to learn that this is known to the Inquisition or even the Deathwatch itself. If they start to shut down the facility they are stopped: Where do they think there experimental ammunition is coming from. Maybe this leads them to a moral dilemma, depending on the style of your group, how 'human' they are playing theire marines.
Furthermore as the Imperium studies the Tyranids, they are starting to understand the Space Marines better. The Kill Team is called to a Tyranid Thread and encounter slaughtered Space Marines. As soon as they also encounter Tyranids they notice that their Toxic quality has significantly increased since the Tyranids have adapted themselves to the physiology of the Space Marines.
At first they have to overcome this highly dangerous thread and furthermore stop the whole Tyranid fleet with communicating to the rest of the Great Devourer to not spread the knowledge about the evolved lethal Toxic Qualtiy.