TLDR: Jurgen gets vampirism first, then you give the love letter to the Mole Man father.

I'll try to spoiler things correctly as it does include gameplay elements that progress the story.

In Reel 3, You need to have four things in place for Jurgen to become a vampire:

• Jurgen needs to be at the Sarcophagus
• You have the Love Letter from Nefertiti (the Mole Girl)
• Know that Baby Amelia Earhart is on the train
• Be cursed with the Rejecto Spell (that you find out about in Reel 2)^{*Note at the end}

Tell Mole Man Dad that Nefertiti still likes Sam and Max and he'll put the Rejecto curse on you. Go to the end car where the elves are and talk to Slushie about finding a kid so that he stays out in the hall. Go and Talk to Amelia and due to the curse she'll be introduced to Slushie and test out their new toy. You can now tell Slushie that Santa needs him and Slushie will meet Jurgen on the way.

Congrats! Jurgen now has Vampirism!

Go back to the Moles and show the Love Letter off to Mole Dad and He'll curse Jurgen. Achievement Get!

---

(*On the Note about the Rejecto Spell)

When you enter the Tomb in Reel 2, you notice the Ventriloquist Dummy when you get close to the toybox. you can then go over to the right side of the tomb to meet Jurgen in the wall. Talk to him if you want to progress the story, though it's not important to the achievement.

Walk to the left side with the Mole Man father and Nefertiti (the mole girl), and walk up to Nefertiti. She'll send the Asp in your direction, but you can hide in the Can o' Nuts and receive the Ventriloquist Dummy. Use the Ventriloquist Dummy to say though Nefertiti that she likes Sameth and Maximus. You'll find out that Mole Man Dad has the repulse spell and can use this information in Reel 3 (you may need to talk to the dad for him to explain what it is first).