Rub pork loin with Achiote Rub. Cover and refrigerate 4 hours.
Place pork in a large roasting pan; arrange beets and onion around pork. Drizzle beets and onion with olive oil; sprinkle with sea salt. Bake at 425° for 1 hour or until a meat thermometer inserted into thickest portion of pork registers 155°. Remove from oven; let stand 10 to 15 minutes or until thermometer registers 160°.
Toss roasted vegetables with sherry vinegar and 1/2 teaspoon salt. Slice pork roast into thick slices. Arrange pork over vegetables and sliced avocado; drizzle with Mamey Coulis.