For my DK Jr kills creens, it was mostly about ignoring the score and following the "Just keep living" mantra MrsJive often uses. Simple, but effective in a lot of cases. Repeating it out loud to myself helped keep me out of my own head, too.
Confidence can help a ton, too. Tim kind of pointed to that when he referred to the novelty of a 1M game wearing off. You know you're good enough, you know the game, you know you can do it eventually, so the pressure is really off in a lot of ways because you know you'll be able to do it on one run or another. For example, Spaceman knows he can get a Crazy Kong KS because he knows the game well enough. So, he should be focusing on the fact he knows it's possible for him to take any one of his four lives all the way to the end instead of worrying.
Another trick I often try to use is telling myself to prep for whatever is next. Ignore the score, the mistake(s) you did or did not make, the miraculous save, etc. I try to use this one especially when I do something exciting or good because the rush that can come with the achievement. Helps me to try and think about what is next to get myself back on track instead of on adrenaline. Naturally, this one can backfire by distracting you from the present, but I still think it can work some people and situations.
