"admirable challenge" is a correct and usable phrase in written English.
You can use it to refer to something that is challenging and admirable, either in the sense that it is difficult yet commendable, or that it is worthy of admiration. For example: It was an admirable challenge for the prospector to make a living in the Klondike at the turn of the 20th century.
There was a fine edge, especially, to the tackling of Wes Brown who made admirable challenges on Hasselbaink and later Gianfranco Zola when an opening goal was feasible.
Move On would not help me promote my work, neither has the Nation, really, or, for that matter, Ben & Jerry, whose work I admired more before they sold their company to a mainstream corporation (although they have been engaged in admirable campaigns challenging military spending for years).
While parliament's recent habit of forging consensus is admirable, the real challenge lies where both parties deeply disagree.
The funding is robust, the goals are admirable and the challenge has engaged lawmakers and school districts to embrace critically essential changes in the way they educate youth.
The resolution by the Parliamentary Assembly of the Organisation for Security and Cooperation in Europe is chiefly admirable because it challenges the Kremlin's attempt to put this area of inquiry off limits.The OSCE resolution is open to legitimate challenge.
Trying to be strong in spite of such challenges is admirable but can cause you to fail long-term, so seek the help that is there for taking.
The ACJW players met these challenges with an admirable fluency.
This is especially admirable in light of the challenges surrounding hosting these vital elections, just weeks after an attempted coup threatened to derail the process.
By contrast, The Times's thorough and sustained coverage of gay rights has a remarkable sense of inclusiveness and solidarity: across sections, from Styles to Sports to Metro, The Times movingly tells the stories of admirable individuals who are overcoming challenges.
Mr. Ford faces a difficult challenge, and his instincts are admirable.
