He was actually winning until Ulic Qel-Droma was captured and Mandalore the Indomitable was killed. Mandalore led the Fourth Battle of Onderon where he was killed. The remainder of the Mandalorians scattered at the loss of their leader, defeated by the alliance of Beast Riders and the Republic.
Then Ulic led the Republic to Yavin 4, where they cornered Exar Kun and imprisoned his spirit on the planet.
Exar Kun was dominating the galaxy, making his way to Coruscant and Tython before he was defeated.
This seems counter intuitive, 'Exar Kun was winning the war until he started losing'. It seems Kuns defeat was due to successive defeats at Onderon and Ossus at the hands of the Republic
. We also have to remember MtI is not in this fight and neither is Qel-Droma. If Kun is so lost without them then surely all MtU needs to do is bombard Yavin 4?