When to use 不是 + adj
But I’m confused as to why 是 is there. I thought negation of
  adjectives should’nt be accompanied by 是. Could someone explain this
  please?


First think the component as 是[other description] where [other description] is true. 是 is used to denote some description is true. Because [other description] is after 是, [other description] is true.

Second think another component as 不[other description] where [other description] is false. 不 is used to denote some description is false. Because [other description] is after 不, [other description] is false.

First point and second point exist independently. Although they exist independently, they can be used together.

Use "first point" first. think 是特別漂亮 as 是[特別漂亮](是[other description], where [other description] is 特別漂亮)(is especially pretty). 是 is used to denote [other description] is true so 特別漂亮(especially pretty) is true. You get that 是特別漂亮 means is especially pretty.

Then use "second point" , think 不是特別漂亮 as 不[是特别漂亮](不[other description], where [other description] is 是特别漂亮) (is not especially pretty). In this example 不 is used to denote [other description] is false so 是特别漂亮(is especially pretty) is false. You get 不是特別漂亮 means "is not especially pretty".