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to challenge to (a fight, game, etc.); to throw down the gauntlet; to contend for
to tackle (e.g. a problem); to attempt; to go after (a prize, record, etc.)
to pressure (someone) for sex; to make advances to
新しい分野に挑む決意を固めました。
I decided to challenge a new field.
難題に挑む前向きな姿勢が大切です。
An attitude of tackling difficult problems is important.
世界記録に挑んで失敗した。
He challenged the world record but failed.