She painstakingly glued the vase back together.

The detectives painstakingly analysed all the evidence.

No. Painstaking is the adjective form. The adverb is painstakingly.

Showing the check made it painstakingly obvious that he had been paid

painstakingly means that you had to try so hard for something that it hurts, usually used in an iconic fashion to describe how hard someone has to work to explain something simple to someone that doesn't get it.

With excruciating detail - perfect in every way ...

painstakingly