In order to survive the battle you need to prepare the Mongoose, for which you need either Ostmurk (which you can get in the cave with the entrance underneath the waterfall), Endrega fetus (which you will get during the Endrega Contract mission) or the Essence of Death (which you can get during In the Claws OF Madness mission).
When ready go with Sheala to the Kayran Lair, use the Mongoose when you still have two steps down left (one step will be too late).
What you need to do is:
1) do not get hit (or at least not directly) by the tentacles; use dodge a lot!
2) do not stand right in front of the beast - try to keep to the far left or right.
3) when close (but not too close) to the right or left tentacles (the ones with the red lights) use Yrden, wait and dodge - when the tentacle is locked with the Sign just keep on attacking the weak spot. Rinse and repeat three times, and the QTE should come up - follow the instructions.
4) after successful QTE the monster should be trapped under the rocks. If you lost vitality just run about, dodge and wait until it's full (or close to). Get tot he far left along the rubble and make your way up, avoid the tentacles! When you reach the end, the cutscene shows the dearth of the monster.
For those who prefer visual guide: check out the youtube video, credit is for Michaljarosz.
Iif you gained the Kayran Trap during Indecent Proposal mission the fight may be a bit easier for you, however I did not use it.
Before giving thumbs down please tell me what to improve!