become

One of the first verbs I learned when I started learning russian was the verb stat' = become.
At the beginning I thought that this verb was used both as sovershennyi and nesovershennyi vid glagol.
Then I discovered the form stanovit'sya.
So if I want to ask: Am I becoming boring?
The translation is: Ya stanovlius' skuchnym / utomitel'nym?

"Стать" - это совершенная форма глагола "становиться".

"Он что сделал?" - "Он стал"
"Он что делает?" - "Он становится"

Translation is correct.

Я становлюсь скучным = I'm becoming boring
Я становлюсь утомительным implies that your opponent or a person you're talking with is getting tired. Just a slight nuance.
Я становлюсь нудным/занудным (boring like a nerd).
Мне становится скучно = I'm getting bored