The windows clipboard works by the sending app offering the data in a number of different formats, and the receiving app the chooses which format it wants to take.
For example, if you are editing a document in MS Word, and you copy some text onto the clipboard, Word will create an offer for Word format, plain text and a number of intermediate formats with varying levels of mark-up support. If you paste the text into another word doc, then Word will accept the text in native format, but if you paste into a simple text editor like vim, then it will take the plain text version.
The point is, that you can't have an image in TIFF format, unless the sending application is offering an image in that format. You might want to experiment with an application that uses TIFF as it's native internal format, and then call EnumFormats() (From Win32::Clipboard) to see if TIFF is offered.
In the general case, you probably won't be offered a TIFF image file by most applications, so if you want to save in that format, you need a conversion libary. fisher suggested Image::Magick which I also think is a good choice.