1. (often in refer, to answering a question directly, answering for sth. etc) to (try to) evade sth. : X виляет хвостом = X is trying to weasel his way out of it
X is hedging (beating around the bush)
(in limited contexts) X is trying to confuse the issue.
2. \Х-26- перед кем to ingratiate o.s. before s.o. , be subservient, try desperately to please s.o. : X виляет хвостом перед Y-ом = X falls all over Y
X kowtows before (to) Y
X kisses up to Y.
Грубый и хамоватый с подчинёнными, он хорошо умел вилять хвостом перед начальством. Rude and boorish to his subordinates, he really knew how to kiss up to the bosses.
Большой русско-английский фразеологический словарь. — М.: ACT-ПРЕСС КНИГА. С.И. Лубенская. 2004.