Take A Run At Meaning

(transitive, idiomatic) To attack or challenge or to try to attack or challenge.

Example: 1989 Nov. 26, Deborah Hofmann, "Fashion: Fluffy Outerwear Invades City Streets," New York Times (retrieved 24 Sep 2012):
  "No one else has achieved the right knit of polyester Dacron fibers—lots of mills have taken a run at it."
2001 Oct. 3, "Faces In The News," forbes.com (retrieved 24 Sep 2012):
  Cisco Chief Executive Officer John Chambers has scarcely hid the fact that his company is actively eyeing a number of acquisitions. At a luncheon in Toronto he felt compelled to deny recent speculation that Cisco would take a run at Canada's Nortel Networks.
2003 Nov. 9, Joe Klein, "Hectoring Is Not Leadership," Time:
  Dean told me that he understood he would have to grow as a candidate in order to succeed, that it was time to move his campaign beyond attacks and anger, to take a run at the vision thing.
2009 June 16, Bob Swanson, "Weather headlines," USA Today (retrieved 24 Sep 2012):
  Through Monday, Honolulu has set record highs 8 days straight and could again take a run at a record today.
1998 March 22, Robert Lipsyte, "Backtalk: New Sign Of Spring—Murdoch," New York Times (retrieved 24 Sep 2012):
  Like a tall dog who attacks a bear to remind himself he is still a tall dog, Ted Turner took a run at Rupert Murdoch last week.
2006 July 24, Hank Gola, "Dimarco Eases Own Pain Eases Own Pain," New York Daily News (retrieved 24 2012):
  Only one guy was brave enough to take a run at Tiger Woods at the British Open yesterday. . . . DiMarco finished two shots behind Woods.