I need to convert my 72dpi illustration to 300dpi

If you made an image [TIFF, PSD etc] with the correct dimensions (i.e. expressed in inches or mm) at 72 PPI and you need the same dimension but at 300ppi you really have to start over - or - accept that pixels are being created to achieve the desired resolution.

You are pretty much making each original pixel into 4 - so even though resolution IS increased detail is not. Sorry

Or was it a Jpeg? That gives more problems - Jpeg files have compression applied, increasing resolution enhances the compression artefacts - this means that Jpeg is only really suitable for final file delivery/transfer - once size and resolution (and any sharpening) have been completed  Jpeg is not OK for archiving or for any file that may need to be resized or cropped down the line. 

I hope this helps
neil barstow, colourmanagement net :: adobe forum volunteer:: co-author: 'getting colour right'
google me "neil barstow colourmanagement" for lots of free articles on colour management

Just start again with enough resolution. You can't add  missing detail by magic; that's like trying to turn chicken soup back into chicken...

DPI/ PPI by itself has no meaning without the actual pixel dimensions. You need to be more specific. DPI is a matter of interpreting the spatial density of pixels, not an actual physical property of any image. In the simplest case just changing the DPI in the image resize dialog without changing the pixels could be enough. It's not really clear what you mean by HQ printing and all that. Even in commercial printing 300 DPI is merely a commonly assumed "standard", but stuff gets printed at lower resolutions all the time depending on the purpose and the technical method used.

Mylenium