Place eggs in a saucepan, cover with water, and bring to a boil. Turn off the heat, cover, and let sit for 10–12 minutes. Transfer to an ice bath, cool completely, then peel.
In a bowl or jar, whisk together hot water, apple cider vinegar, beet powder, sugar, onion powder, and salt until the beet powder dissolves. smooth.
Add peeled eggs to the liquid, ensuring they’re fully submerged. Refrigerate for 4–12 hours (overnight gives the best color and flavor).
Pat eggs dry, slice in half lengthwise, and remove yolks. Mash yolks with mayonnaise, horseradish, Dijon mustard, and vinegar or lemon juice until smooth and creamy.
Season with salt and pepper to taste. Garnish with dill.