This question has been asked before. Here is the top-voted answer:

/u/Cruentum

Genghis Khan fought against Jamukha three times in The Secret History (though really only twice with Jamukha as head commander). The first time was in 1187 during the battle of Dalan Balzhat which started when Jamukha's brother was killed after leading raids on lands in Temujin's territory, Jamukha demanded the killer and Temujin refused. And the ensuing battle Temujin was routed and retreated to the Onon River while Jamukha supposedly boiled the survivors in cauldrons. The loss of this battle resulted in the Jurkins (not the Jurchens of Manchuria of course, who were under the Jin Empire) revolting against Temujin.

In 1201 however, Jamukha was elected Gurkhan of the surviving Taichi'uts, Tartar and the Merkits (the Tartar and Merkits being clans defeated by Temujin and the Wang Khan) who demanded that he defeat Temujin. Temujin secured an alliance with the Wang Khan and they defeated Jamukha in the battle of Thirteen Sides/Koyitan (Frozen Field) (in reality Temujin was actually the minor part of the battle securing the sides as the Wang Khan also wanted to halt his rising influence). The battle actually was so fierce that Temujin was forced to send in his personal bodyguard which nearly resulted in him getting assassinated by a poisoned arrow, supposedly by Jebe, because of the lack of men guarding him. The most important thing he did in his battle was actually wiping out the Taichi'uts, the branch of the Mongols who refused to acknowledge Temujin as khan and left him.

However by 1203 the Wang Khan and Temujin's relationship were different. Temujin was now the second strongest force in the Steppe. Jamukha now allied himself with Wang Khan's son and began sowing the idea to attack the Mongols. And that's how the battle of Kalakhaljhid/Kalakalzit Sands occured. The fighting supposedly lasted for multiple days and Temujin began thinking the battle just started becoming mindless chaos after hearing Bo'orchu, Borokhula, and even Ogedei nearly died and ordered a retreat. The Wang Khan however could not capitalize because the losses were too high and his son, Senggum, was injured in the battle. Supposedly, this loss was disastrous, that Temujin had to flee with all his men to the other side of Mongolia, in Baljuna, a swamp, where his men supposedly pledged eternal loyalty to him though whether or not this actually happened is up for debate[1] .

After this Jamukha was attacked by the Wang Khan after he found out Jamukha may have been plotting to usurp him and the fleeing Jadarats went to the Naimans, who Jamukha also betrayed before finally being betrayed by his own Jadarats. Who took him prisoner and brought him to Temujin who famously ordered the execution of all of them.

The folowing battle between Temujin and Wang Khan (it started with the Wang Khan catching Kasar's army out of position) resulted in Temujin's victory and the Wang Khan tried retreating to the Naiman's who killed him, while Senggum tried fleeing to Kashgar but was killed. Either way, Genghis definitly lost the first and third battle.