What's the best way to expression your accomplishments without sounding boastful?

You ask - and show interest about things they've accomplished, first. It's polite, and it shows them that you're interested in them, too, rather than just talking about yourself. BUT, you can't just ask "what have you accomplished ?" because not everyone's accomplished things, you ask about their life and get to know them, then if they ask about you slowly tell them the accomplishments you're excited about. The key point is BE MODEST! (:
I hope all is well, and you pass! Good luck, rockstar! (:

The answer is true a pertinent question is an appropriate question.