There's nothing enjoyable about hard conversations, so much so a lot of us will do anything to postpone or otherwise avoid them. Inevitably, however, this is a bad idea, so instead of dodging around, square your shoulders, take a deep breath and employ these tips to help get through it.
Before you do anything you should "visualise the end", according to author and workplace consultant Ana Homayoun, writing for Fast Company:
...step back and think about the ultimate goal and your ideal outcome. Doing so can help keep you focused and calm in the face of overwhelming details.
Starting the conversation can seem like the difficult part, but Homayoun is right: figure out what you want to happen first.
On the same topic, she also recommends coming up with multiple solutions. If it's a hard talk, some sort of compromise will almost certainly be on the table.
You may also have to "reset your attitude":
The mental and emotional state with which we approach tough conversations matters. For some, meditating or visualising solutions helps; for others, writing down potential solutions and benefits can lead to feeling more open and relaxed. Hitting your mental “reset” button, in whatever way works best for you, can help you project a better outward demeanour.
I would further add that, given the type of conversation, consider the fact you might be wrong. Don't be stubborn — if you realise this halfway through the conversation, just admit it and work from there, rather than continuing to fight on unsteady ground.
By the same token, if the opposite is true and you're not making headway, don't be afraid to disengage (if appropriate), so the other party or parties can have time to think on your points, as it's easy to lose sight of things in the heat of the moment.