Baidar was the second son of Chagatai Khan. He participated in the European campaign (The elder boys campaign as it was known in Mongolia) with his nephew Büri from 1235-1241. He commanded the Mongol army assigned to Poland with Kadan and, probably, Orda Khan.
Baidar defeated many Poles, Russians, Germans and Moravians. On 13 February 1241 the Mongols crossed the frozen Vistula. The town of Sandomierz was taken and plundered. Further to the west, on 18 March Orda and Baidar met the Polish army under the command of Duke Boleslaw V (not present at the battle) at the battle of Chmielnik. The Poles were heavily defeated and Boleslaw with a part of his troops fled to Moravia. On 22 March the Mongols stood before Kraków, many of whose inhabitants had already made their escape. On Palm Sunday the Mongols set the town on fire and took prisoner large numbers of the people who had remained. Moving further west, Orda and Baidar reached a place east of Opole, where they forced Duke Miecislaw's army to retreat. Near Racibórz they crossed the Oder. Racibórz was burnt by its inhabitants when they left the town. Breslau (present-day Wrocław) fell into the hands of the Mongols, although the citadel itself did not surrender. Their first assault against the fortress having failed, the Mongols wasted no time on a siege. They bypassed the citadel and pushed forward to the west.
After defeating a combined force of Poles, Germans, Templars and Teutonic Knights at Liegnica (see Battle of Legnica), Baidar camped for about two weeks in the neighbourhood of Othmachau (between Opole and Kłodzko). Early in May 1241 they entered Moravia. Various small, unprotected places were plundered. When an attempt to take the town of Olomouc came to nothing they joined, via Brno, Batu's main army in Hungary. Although Bohemia remained unmolested, Moravia had much to endure. The destruction in Poland, Silesia and Moravia was all much of the same kind.
Some European chronicles claim Baidar was killed near Olmutz in 1240, but these records appear to have been inaccurate, as Baidar later participated in the election of Güyük Khan in 1247.
Leo de Hartog (2004). Genghis Khan: Conqueror of the World. Tauris Parke Paperbacks. ISBN 1860649726. http://books.google.com.pe/books?id=a4p9C6J35XYC&printsec=frontcover&dq=Genghis+Khan:+Conqueror+of+the+World&hl=es&ei=f8RsTsa3DoqcgQe_v-TdAg&sa=X&oi=book_result&ct=result&resnum=1&ved=0CCwQ6AEwAA#v=onepage&q&f=false.