1) To the person who makes the hiring decision, make it clear that the person sucks up more money than they make the company. Make it a pure business decision.
2) Make it easy - very few people enjoy firing people. It is not only confrontational, but it often means admitting you were wrong in hiring in the first place. Give your boss as much of an emotional out as possible.
3) Have the meeting where you solidly and without malice make your case. If your boss isn't going to fire the guy right then and there, but until X, Y, or Z are completed then your boss is going to pussy out. Institutional inertia will set in. Say "I appreciate that you're in a tight spot with this project. What can we do to make this work." When it doesn't work, have a follow up meeting that puts the decision not to fire back in your bosses line of sight, and show that, indeed, it's continuing to not work out. Do NOT say "I told you so." You'll just make your boss resistant.
4) Once the problematic developer is gone, have a follow up discussion that shows it was the right call. Again, don't say I told you so. Say "Thanks for taking care of that. I know it was tough, but it's really working out"
Your job is to make your boss look good by kicking this person to the curb. You're approaching your boss and assisting them in making an informed decision.
Of course, if you're just trying to get someone fired out of spite, that's trickier.