It’s important to check things, but don’t check them ‘detaily’. It is not a word in English. If you want to use an adverb to describe how well you check things you can use the word ‘thoroughly.’ That said, non-natives don’t like the word because it’s quite a difficult one to say!
Alternatively, why not use the phrase ‘in detail’. It is just as common and much easier to deal with. Importantly, it goes at the end of the clause. So, instead of „My boss in detail checks everything“, you would say, „My boss checks everything in detail.“
Here are both options together:
A: Have you looked through the document thoroughly?
B: Yes, boss, I have checked everything in detail.