Getting Giger with anything is very tricky. It's either too much of the original subject (Tinkerbell) or everything is Giger.
I gave it a quick try myself and had to add a LOT of style references to various Giger art and an image input of Tinkerbell.
Prompt: https://www.cartoonbucket.com/wp-content/uploads/2015/08/Tinkerbell-Flying.jpg monochrome ink illustration of tinkerbell, in the style of H.R. Giger --ar 4:3 --sref https://wallpapercave.com/wp/E5T5C2Y.jpg https://artsy-media-uploads.s3.amazonaws.com/Rm-xzSgX1aKj62WiX-vxWg/1974-B-250++Li+I.jpg https://wahooart.com/Art.nsf/O/A25T9V/$File/H.R._Giger-hr_giger_landscape_XXVIII.JPG --stylize 55 --iw 0.8
The URL's were just the first that popped up on a quick search for Tinkerbell and H.R. Giger.