It's my breathing I'm struggling with, my lungs start to hurt. Any tips for keeping that steady?
This is a more in-depth thing than just "try X, Y and Z". The breathing thing has a lot to do with psychology. In a nutshell, it's realising
â—‹ you can control your breathing rather than it controlling you (and making you slow down) when your running.
â—‹ getting very out of breath and your heart rate maxing-out is a Good Thing. It needs to happen and you you don't need to be concerned about it.
So to control your own breathing when you are running, don't automatically assume you need you slow down. Make sure your head is still, your shoulders relaxed and your hands not tensed. Keep your chest and core (torso) still, no up-down movement. The tension in your body wastes energy and makes you more exhausted. It also stops you from relaxing.
Relaxing during a run is a physiological thing, not just physical. Thinking "I can't do this, I need to stop, I'm too tired" and del that negative self-talk becomes self forfilling. Tell yourself you are strong, fit, healthy. Or distract yourself. Try to think of something completely separate to running - plan dinner, think about wording an email you have to write. One of my favourites is imagining I am training someone else. In fact, over the last two days my mind has wandered during a run thinking about how to word this reply I'm writing now 
Relaxing is how you get control of your breathing. Physically relaxing in your run and mentally relaxing to become calm and quiet.
But sometimes you do all of this and will still have very laboured breathing and a high heart rate. So you should, you are exercising hard
I don't want to teach grandma to suck eggs here, but do you know about hear rate zones?
You have your normal, resting heart-rate. You then have three zones when you are active.
• Fat-burning zone
This is the low-to-medium intensity exercise zone. It's when you're active, but not pushing your muscles - like fast walking.
• Cardio zone
This is the medium-to-high intensity exercise zone. It's when you're pushing yourself but not straining. Most of your run will be here.
• Peak zone
This is the high-intensity exercise zone. Its whrn your breathing is laboured, your heart beating fast and youllbe sweating a lot. The peak zone is when you improve performance and speed.
You don't want to spend long periods of time in peak zone, but it's necessary for you to improve.
If you were inclined to pay a personal trainer to get you fit, one of the things they do is to push you to the peak zone and try to get a bit more out of you in there ("don't stop yet, 500 more meters", "Faster, faster, come on", "push push, push yourself to get to the gate over there" etc)
Right now you are training your stamina as you move from Week 7 to Week 9, so you can run for longer. Getting into the peak zone is necessary for that, peak zone is when change happens. It means your body is pushing itself. It means you're "training" rather than just "exercising".
Throughout the C25K programe you are definitely "training" - you are teaching your body to do something you couldn't do 3 months ago. You're constantly pushing to run for longer, so you will get to peak zone and have laboured breathing. That's not a problem, it means it's working
When you finish C25K, then things may change. You may decide you are just going to run for half an hour as exercise and that's all. In which case you may go back to just cardio zone exercise. Or you might try to increase your pace and speed even further (increase distance to 5k or beyond, or work on getting faster times). That will involve peak zone running too - running when your breathing is laboured, you're sweating buckets and feel like you might collapse at the end.
So, very long essay to basically say, if you're breathing is hurting:
(1) check your running style. Still, calm and not tense so you don't waste any energy
(2) use controlled breathing techniques to try to relax further and control your breathing rather than it controlling you (big breaths, controlled breathing to a regular count etc).
(3) Distract yourself by thinking about something else. Use positive self-talk
(4) Assess how far near the end of your run you are. Pushing yourself to the max for the final 5/10/15 mins (whatever you can manage) will improve your training if you can manage it. So don't worry about laboured breathing now, rest when you're done.
(5) Ask yourself if you're trying to push yourself. If you're aiming to get a fast time, run further, run longer - you will push to the max and that might mean breathing so hard it hurts. Sometimes have 'easy' runs when you don't push yourself. Sometimes 'go for it' and accept it will be hard graft, but worth it when you see results
and then...
(6) if you've gone through all of these and are still concerned about your laboured breathing..... then slow down your pace because you're probably going too fast.