You need to collect four Wrapped candies and activating the UFO will zap and collect three of them for you. This means you don’t have to worry about making Wrapped candies too much.
Since you need to make five Striped candies in 15 moves you should mainly focus on collecting this order.
To make it easier to make special candies you should clear the Icing as quickly as you can. With each one you clear it will become increasingly easier to make special candies.
When you can’t make a Wrapped or Striped candy match candies near the bottom of the playing field. Although the playing field is small, matching near the bottom will shift the largest amount of candies. This in turn will hopefully start a chain reaction that will create new opportunities to make special candies.