An insecure process server becomes the target of a serial killer and teams up with a private investigator to catch the killer and regains his self confidence.

Yes, I would get rid of the "regains his self-confidence" part, mainly because your description of the protagonist as "insecure" implies the inner journey he'll be taking anyway.

Also, now you have room to describe the actual story more. Either why he is a target, or what kind of serial killer it is (which might suggest why the protagonist is a target). You might also want to attach an adjective to the PI if there's a buddy relationship that is explored. Maybe he's hardened, volatile, disillusioned, risk-taking, whatever...

The character's inner journey should not form part of your logline except if it's the?main plotline of the story.

To rephrase your logline, I would ask the question: why is the process server?the target of a serial killer?

An insecure person has no self confidence to regain as they never had it. You need a different word for regain or ?change the protag description.