Hi [USER=135828]@samsimon[/USER]
You might need to share a PSD file for forum members to examine to get good recommendations.
It depends on what is causing the soft edges. If it is only in the Layer Masks, then its possible that just applying a Threshold adjustment to the Mask would sharpen things up.
If the softness is in the transparency layer build into the pixel Layer, that too could be extracted to a Layer Mask and also sharpened with a Threshold adjustment Layer
If the softness is in the pixel data itself, they that would need some level of sharpening applied to the pixels. Topaz AI Sharpen does a pretty good job yet there are others
When you mention Adobe Illustrator (AI), are you referring to converting to vector images? AI can also handled rasterized images so depends on what you want. If you want to convert to vectors, that is a bit more involved and again very specific to the type of image you have. I don't know how to convert directly to AI format yet they more standard approach if you have created shapes or vectors in PS, is to export to EPS format which can be read into AI.
To be more specific, seeing representative PSD files would be helpful to determine what is possible for sharpening and then more specific needs such as needing raster images in vector format or just moving raster images into AI.
Will wait for more details from you and either I and/or other forum members should be able to jump in with more suggestions.
John Wheeler