"Go in swinging hard" is a fighting or boxing reference, and it means to start swinging and hitting before the opponent has had a chance to start swinging at you. Here's it's being used figuratively. It probably means to start a conversation with children about "Teddy tablets" by giving a strong warning about their dangers, without first finding out if they children know anything about the drug or have any curiosity about it. The article says you simply must talk to your children about them, but not by "going in swinging hard."

It means to be really forceful with an argument or conjecture, to insist on its importance or correctness. Hope this helps