Do bosses in Bloodborne become stronger when you lvl up?

Yesterday I started playing Bloodborne (and it quickly forced me to fall in love with it) and I haven't found many difficulties beating the first boss (Cleric Beast) and reaching Father Gascoigne.

This hunter instead is giving me nightmares. I've spent two hours trying to beat him (and this includes various runs to farm echoes to upgrade my Saw Cleaver and level up) but nothing. He always beats me...

My tactic is this: stay behind gravestones and wait for him to be close -> hit him with R2 -> wait for him to transform -> play the carillon -> visceral attack -> molotov.

I always come ONE R1 hit from killing him. But he always manages to kill me before that hit.

So I was wondering: if I do multiple runs to farm a decent amount of echoes and level up will Father Gascoigne be stronger or his attributes are always the same? If I'm lvl 10 his stats are the same than if I'm lvl 20?

No, enemies and bosses don't scale with your level.

Enemy strength is fixed to the area, so you can level as much as you want.
Be warned, though, even at high levels, enemies can still easily kill you.

Note: Insight will make some enemies more dangerous because they gain new and more powerful attacks.

Sources: Reddit
Gamefaqs question
Gamefaqs thread
Gamefaqs thread 2
My own expirience