Contract: Swamp Thing

Contract: Swamp Thing is a contract in Velen. A creature in Crookback Bog is terrorizing the nearby town. Go meet the man that posted the notice in the swamp. He says something in the fog is taking people and never letting them leave. You can haggle with him before entering the swamp. The base price is 249 and can go up to 339. When you settle on a price, head off into the swamp to find the mysterious fog.
 * Contract: Monster from the Swamp
 * Anyone knows how to read, read this, and read it careful, so that it's known far and wide, or at least throughout the whole village. 

Out in the bog, by where we dig peat, there's a beast what feeds on men and spurts out deadly mists all around itself. If you're good with a sword and looking for coin, know that I'll pay and pay well for that beast's head. And to everyone else, stay out of that accursed bog if you value your lives. Don't say I didn't warn you. 
 * -Leslav

Journal entry
''Near the village called Downwarren, Geralt came across a man who dug peat for a living. One glance was enough to know something was ailing the poor fellow. He warned the witcher about a strangling fog which had sprung up in the nearby swamp. The man's story convinced Geralt a monster was at work and so he decided to look into the matter.''

''Geralt's investigation took him to the very heart of the swamp. As he was walking an exceptionally hideous foglet suddenly jumped out at him from an unusually thick patch of fog. The monster was old and strong, making defeating of it no easy labor. Geralt managed the task, however, and a few moments after the foglet breathed its last, the poisonous fog dispersed and the witcher could at last fill his lungs safely.''

If Geralt insists on payment immediately

''Hoping to find someone who would offer him a reward, Geralt went to Downwarren. A peat digger residing in that village was grateful Geralt had enabled a return to his labors and so handed the witcher some coin.''

If Geralt waits a week for payment

''Hoping to find someone who would offer him a reward, Geralt went to Downwarren. A peat digger residing there was grateful to the witcher for enabling him to return to his labors and promised the witcher a generous reward - if he could stand to wait a few days while he gathered more funds. Geralt agreed, and in return for his patience received a purse full of gold crowns.''

Basics
Follow the marker on your mini map, fighting any drowners  you see along the way. You will arrive at the spooky fog soon enough. When you enter, Geralt will have a tough time breathing. Don’t worry about losing health. When you find the hut in the middle of the fog, you gain back any lost oxygen. Loot the hut and go off to a nearby rock face. There is an illusion blocking the cave entrance. Use the The Eye Of Nehaleni from Keira Metz and go inside. You’ll soon encounter a foglet. Quickly slay it then arm your blade with Necrophage oil. It will help in the upcoming fight. Make sure to loot a nearby chest for new recipes and diagrams. When you’re all set, continue in the cave to meet Ignis Fatuus. Ignis Fatuus can be a tough fight, especially if you aren’t the advised level 12 for the contract.

His hits take a lot of damage, so play it safe by dodging and using the Quen sign. The monster cannot leave the fog, so run off to regenerate health with a Swallow potion if you need to.

When fighting Ignis Fatuus, he will disappear into the fog often. Keep an eye on the denser clouds of fog to track him. He will also summon level 0 foggiest to distract you. Hit them once to get rid of them. Go in for attacks after Ignis Fatuus lunges and then dodge. Keep this up until he is dead. Using Thunderstruck potion can help speed up the fight as well. When the “swamp thing” is dead, cut off his head as proof and leave the cave. Go back to the man who issued the contract and claim your reward.

Trivia

 * If you haggled with him for a higher price, he will not have it all when you come to collect. He does promise to pay it all with interest in one week’s time. Let him pay you then instead of now, so you get double the reward. Just meditate for seven in-game days to claim your reward.