Achievements are Battle.net Account bound, so having multiple WoW accounts on one Battle.net (you can have up to 8 WoW accounts), those are already a part of things there.
Moving a character from number 1 WoW account to number 2 WoW account within the same Battle.net isn’t going to have any effect on that for you.
You can find some more info here in the Character Transfer FAQ, select WoW account in the drop down there.