Start a new career with a new, player, don't choose already exisiting player since then you won't have neutral reputation.
Reputation is related to your reactions after points. You can either choose a positive reaction ( by pressing Y on the keyboard) or a negative reaction (by pressing H on the keyboard).
For this achievement, you should keep on spamming negative reactions whenever you can. This way you will get your full negative reputation fast. You can also choose bad responses at press conferences, which will also make your reputation lower.