technically Shikamaru didn't defeat Tayuya, Temari did. after Shikamaru and Tayuya fight for awhile Temari came and helped Shikamaru. She performed an animal summoning and defeated Tayuya.
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Tayuya had a fight with shikamaru and was almost able to kill him but Temari, however, arrived at the last second, and killed Tayuya first by using her Summoning: Quick Beheading Dance to destroy the forest, causing the sliced trees to fall on Tayuya and crush her.
It's Naruto EP 217 (Sand Alliance with Leaf Shinobi). Summary: Gaara's student is kidnapped in a plot to defeat Gaara and capture the One Tails. Assistance is requested from the Leaf when the kidnappers head toward the Land of Fire. Shikamaru is tasked with leading a team to backup the Sand Shinobi (Gaara, Kankuro, and Temari). Shikamaru sees this as an opprotunity to "pay back a debt" from when the Sand Shinobi assited Shikamaru (fighting Tayuya), Lee, and Kiba durning the pursue of Sasuke.
it is never revealed ..................
Nobody.
Ino, Shikamaru, Chouji Asuma