'Play hardball' is an expression meaning to maintain a firm and determined position in order to get what you want. If you 'play hardball' you may behave in an unpleasant or threatening way. This expression is often used to talk about someone who is is is difficult to negotiate with because of being unwilling to exchange or relinquished anything. This expression is more popular in the US  it is considered an informal phrase.

1. Kate felt that she had no choice but to start playing hardball with her roommate over her failure to do her share of the chores because speaking to her nicely about it had not worked.
2. I put in a good offer for the house but the agent decided to play hardball and put me off dealing with her.

1. Tom is a really nice guy, but he can play hardball when he needs to. That's what makes him such an effective negotiator when there's a deal to be closed.
2. Staff played hardball with the company by going on strike. They hoped that such a drastic action would make their complaints more likely to be taken on board.