The best way to permanently delete Google history is to use the Clear History option from Chrome itself. This does not delete the History file (which can be restored with data recovery tools) but rather wipes the data from it. Which is much harder to reverse.
Even with sync, Google will take care to delete the history for all your devices registered to the same Google account. The only thing to watch out for then is the DNS cache. Clean that up and your browsing history is permanently removed.