After finally beating the Kayran, here are some tips on killing the beast.
You need to trap the tentacles using the Yrden sign (The 4 tentacles with the slightly glowing, thicker part). You can only trap the 4 rear tentacles with the glowing part, the front tentacles of the Kayran cannot be trapped!. If you crafted a Kayran trap, you can use that one for the first tentacle, the location is highlighted if you have the trap in your inventory. You need to place an Yrden trap at a location where the tentacle will hit the ground. The easiest way to achieve this is to stand in the same location as the trap, once the Kayran lifts its tentacles, immediately roll to the side. The tentacle will hit the trap and you can sever it.
Avoiding the tentacles is important, a direct hit can do a lot of damage. Watch the pattern, you'll quickly notice when the Kayran lifts its tentacles and it is time to evade. Sometimes it also hits you from the side with a tentacle, but I haven't found what triggers this attack. You also shouldn't stand directly in front of the Kayrans mouth, it can perform an attack that poisons you (if you didn't drink the Mongoose potion) and immobilizes you.
You can also use the Quen sign to protect yourself from damage, but you have to time the casting right or you'll just be hit by a tentacle while or shortly after casting it.
After severing the third tentacle you get a quicktime event (right click, repeated left clicks and space) which will cause parts of the old bridge to collapse. The Kayran now throws stones after you. You need to go to the left and go up the fallen down part of the bridge that now leads directly onto the Kayran. And then you've finished this fight. Don't forget to loot the Kayran for reagents and crafting material.
Push Letho away with Aard, immediately follow that with strong or fast attacks for approximately 2-3 hits, repeat the process until you run out of Vigor; when that happens, run away. If Letho puts Quen up, set a Yrden in front of you to tear it away and buy you some breathing room. Don't attack Letho up close unless you're absolutely sure you want to, and make sure you parry and attack only when he isn't. If you can stun him by parrying, excellent, but only parry when you're just about to be hit by one of his blows. Also, make sure you're using the Steel sword, as it's more effective against humans. You can also set up a few traps quickly if you wish, and ALWAYS dodge to the right just before the battle begins, so Geralt can shift away from Letho's Aard if that's his first move.
Best Answer
The adrenaline bar is activated once you learn your first ability which requires/uses adrenaline.
Also see in the Witcher wiki: Adrenaline Rush
The three skill trees will give you different abilities which are activateable with X (in the case you play with a gamepad directional button up):
This answer is also interesting and provides a screenshot of the adrenaline bar: https://gaming.stackexchange.com/a/178593