The Beast of Toussaint - Blood and Wine
This quest will automatically begin after you complete the Envoys, Wineboys quest. During the first part of this quest you will automatically be thrown into combat against a Golyat enemy (pictured above). He has some very slow attacks but they will hurt a lot if they manage to hit you.
If you want to get in a lot of cheap hits, I recommend the Northern Wind Bomb. It's not on his list of weaknesses in the Bestiary but it effects him as if it were.
Golyat Weaknesses: Ogrid Oil, Quen, Northern Wind (Bomb)
Once the beast is defeated there will be a scene, after which you'll need to follow Milton to the next attack site and investigate things here. When you arrive the first thing you'll want to check is the foot prints on the ground by the boxes. This will update your quest and send you to the south, following the shoreline.
You'll run into some Scurver enemies which are basically Drowned Dead/Drowners combined with Rotfiends. They work like Drowners except that when they're very low on health they explode like Rotfiends. Search the shoreline in the area you fight these guys using your Witcher Senses. You'll find many things that glow red in this area; the drag marks/boat landing marks by the shore are the main thing you need to find.
In the water you'll have to search one of the posts attached to the net for a Monogrammed Handkerchief (pictured above). Once you've done all of the investigating you need to on the shore you'll notice that you have an audience at the inn during a scene. Follow Milton over there and speak with the people inside of the inn to ask which way the ship went that was here.
After a bit of dialogue here your quest will update again, this time sending you nearby to Corvo Bianco Vineyard, a Signpost/location nearby. This is the first time you'll have the freedom to explore and do whatever you want in the Blood and Wine expansion too. You don't immediately have to head over to Corvo Bianco Vineyard.
When you do arrive here, inspect a few of the bodies scattered about the courtyard to update the quest, then head into the cellar when you're ready to fight the Bruxa.
Bruxae Weaknesses: Moon Dust, Vampire Oil, Black Blood, Yrden
She teleports around the room and likes to do a screeching knock back attack that is difficult to avoid. Aard will knock her down and interrupt this knock back, which is your only real defense for it. Black Blood helps for this fight too, especially when she bites you. If you stay close to her for too long she'll leap onto Geralt and bite him, Black Blood will cause this bite to greatly hurt her.
Once she is defeated inspect the body that she was eating before you entered the room. You'll receive EXP for each part of the body you investigate so be thorough! When you're done exit the cellar the same way you came in. Our next destination is the Tourney Grounds which are a little bit to the south of our current position.
At the Tourney Grounds you'll be looking for Palmerin who you will need to talk to for an escort to the Duchess of the Battle Arena. If Palmerin is currently walking about then wait until he stops near the rock outside the arena, this is when you can speak with him.
The Shaelmaar will do a roll attack which will quickly allow him to move around the arena (you must dodge this roll) as well as a ground slam attack which sends out a shockwave that you must dodge. The rest of its attacks are generally very easy to avoid unless your name is Baron Palmerin de Launfal. Then you just stand next to the Shaelmaar as it performs easy to dodge attacks and get yourself knocked out.
**Important** Even if Palmerin drops down to 0 health during this fight he will not actually die. Don't worry about keeping him alive, he's an idiot, yes I know.
Shaelmaar Weaknesses: Samum (Bomb), Relict Oil and Aard
Once you've gotten the Shaelmaar down to a sliver of health the fight will end and you'll be given the option of killing or sparing the beast. If you're going for the Embodiment of Five Virtues Trophy/Achievement then you'll want to spare it.
There will be a bunch of dialogue and scenes after the fight is over, answer whatever you wish it doesn't matter. When you regain control of Geralt you'll be riding on a horse following the duchess through Beauclair Palace. At this point in time you'll also receive two secondary quests; No Place Like Home as well as The Warble of a Smitten Knight.
The duchess will give you two tasks, retrieve the "unicorns" horn and get the golden fish from the lake. For the golden fish all you need to do is dive into the water and retrieve it, most of the fish underwater contain some sort of Candy - the fish you're searching for is close to the surface, near a boat and close to shore. When you get close to the correct fish a scene will automatically trigger. The "unicorn" part takes a little bit more finesse.
After you try to steal the horn from the "unicorn" without any treats it'll flee from you. Use your Witcher Senses and grab a nearby Apple or basket of Carrots. The cookie or any sweets will not work, alternatively you can also use Axii to calm the horse if you'd like as well.
Once you've completed both of these tasks return to the Duchess whose location is marked on your compass/map and another scene will automatically begin. During the chase scene where Geralt is running after the killer you'll complete this quest and automatically begin the next one, Blood Run.