a) to end a series of defeats

German translation:

break a duck = eine Pechsträhne beenden

Sample Text:

The manager has been scarred by each of his previous matches away to German opposition, six trips to the country with three different clubs having ended in defeat. This was an emphatic way to BREAK THAT DUCK.

(The Guardian)---Sergio Garcia Tries To BREAK THE DUCK(deadspin.com sports news portal)