I've found in my life that obstacles and difficulties tend to make us elicit some type of emotional reaction. Those who most succeed are almost always the ones who are able to keep their base emotions in check.
It's a principle I first learned (I believe) while reading Sun Tzu's "Art of war" –which is one of my favorite books to this day.
Keeping these emotions in check is not a stoic, steely, emotion-less face that you put on whenever things get difficult. Rather, it's the ability to feel the emotions taking over and telling them "No."
That big client pitch isn't going to kill you whether you get the job or not. There's always another job opportunity if the interview doesn't go your way. If I had a dollar for ever time I hear about somebody's "dream" job that turned out to be a nightmare, I'd have about a hundred bucks.
Learn to embrace the challenge by not allowing the challenge to strangle you.
The challenge will never strangle you when you can exhibit control of your emotions and response when things get tough.
You don't want a pilot who has an emotional meltdown when something goes wrong at 35,000 feet in the air. The best pilots calmly assess the situation and implement a plan.
The same can be said for surgeons, firefighters, policemen, soldiers, astronauts, etc...
Grace under fire is a beautiful (and useful!) attribute.