How to remove Broken Link Checker widget from admin menu

The problem is probably just that your code runs before broken links checker adds the meta box. Try changing the action line to this:

if(is_admin()){
  add_action('wp_dashboard_setup', 'remove_dashboard_widgets', 1000 );
}

EDIT

To be a little more clear, the particular issue here is that the add_action() function is running super early compared to Broken Link Checker’s add_action function. The two ways to fix that issue are to either run your code later (hooking your plugin’s main functionality onto init and throwing your actions and filters into that init function), or increasing the precedence of your action (what I suggested above).