When I finish the quest For the Republic, part 2 - the game doesn't give an achievement, maybe it's because during the quest I made peace with the Brotherhood of Steel?

For this achievement you have to solve the NCR's problems:

After completing the first two NCR quests, (Things That Go Boom and Kings' Gambit), head to Hoover Dam and talk to Colonel Moore.
You will now have to deal with the Great Khans, the Omertas, Mr. House and the Brotherhood of Steel. Your last objective will be to protect President Kimball, now report back.

How you solve the problems should be up to you, if the solution you choosed is a problem your questgiver will point it out. Making peace with the Brotherhood shouldn't cause problems.

If you still don't get it might be a bug and sometimes earlier decsions cause problems...

Here is a nice decription, complete with decisions that cause problems and known bugs:
https://fallout.gamepedia.com/For_the_Republic,_Part_2


Edit I: removed typos

I Do Everything But Still Only Get [you'll know it when it happens]
I were try 6 times even try by kill everybody in Brotherhood of Steel and still nothing

If you get the "you'll kow if it happens" you did everything right and you should be able to finish the game with the NCR and get the "you will know it, when it happens Achievment", and you should get the "For the Republic"-Achievment
after reporting back to moore before getting "you'll know..."

So it's a bug or you blocked yourself by a past desicion, like working for Yesman to long...

If the Achievment is so important to you you can try to fix it via console as you can finish or resett the questlines.
[url=https://fallout.fandom.com/wiki/Fallout:_New_Vegas_console_commands]https://fallout.fandom.com/wiki/Fallout:_New_Vegas_console_commands[/url]

Is it not so that you usually need to play a game several times to get all achievements. In a second playthrough you can go straight for the few achievements you still lack.

End Sex