I think Kairos has never won a round of combat in our games. Or at least has been, in the words of Darth Vader: "All too easy."
Snippets from my logs:
"Assassin fails at the Garden of Nurgle, but doesn't get hit with a crippling corruption, so she doesn't really mind, passing through the Fortress of Khorne and Maze of Tzeentch unhindered. But it seems Kairos is ready for her, packing cunning 11 in the first battle, yet she easily defeats him, using a Power card to clean up her corruption. Kairos gets only slightly tougher, cunning 13, but loses anyways. Third battle, Assassin uses Ambush to guarantee her victory by denying Kairos, cunning 16 from rolling a die and winning. Fourth battle, Kairos regresses, down to cunning 15 and the Assassin uses her double cunning Power card to hit cunning 30. Kairos fails to explode his die and the Assassin wins."
"All the Inquisitor can do is hope the Captain fails and he might have a shot. Sadly, Kairos doesn't seem up to the task, having only strength seven in the first two battles, which the Captain wins without rolling. Even strength 11 proves insufficient and the Captain has yet to touch a die, but he does complete a Mission, gaining another four Power cards. Fourth battle, Kairos is up to strength 16, but the Captain calmly doubles his strength total to 27 and plays a Power card preventing Kairos from rolling a die, thus completing his rout by defeating Kairos four times without rolling a die once in the confrontations, winning handily." (hilarious)
"Psyker passes too, then the Canoness makes her way through the Fortress of Khorne, but the Ogryn is up next and he reaches the center of the Warp Rift to confront Kairos. Instead of picking willpower, which is his highest attribute at 15 in battle, Ogryn picks strength. Since Kairos cannot explode his dice in strength battles, the Ogryn wins the first two rounds easily, against strength four and strength eight Kairos. Continuing to pick strength, Ogryn defeats a strength 13 Kairos without having to use his Power card or a token from his special ability. Final round, Kairos is pulling out all the stops at strength 22, but without exploding dice and hampered by a Cloud of Flies from the Ogryn, who in turn explodes three times, Kairos is defeated and the Ogryn wins."
"However, as the Assassin is already preparing for her assault, the others can only watch and hope she is vanquished, which doesn't seem that likely. First battle, Kairos is utterly overwhelmed, as he is in the second battle, although the Assassin does use a charge from her Executor Pistol. Third battle sees her win after using the last charges from her Executor Pistol and Frag Grenades and as Kairos goes up to 20 cunning for the fourth battle, situation seems to be turning. But the Assassin uses a Power card to double her cunning, which means she is at 26 vs 20 and with Kairos rolling a five, she doesn't even need to roll to finish Kairos, winning in under an hour."
"Rogue Trader enters the Palace of Slaanesh, but that's as far as he gets, as the Canoness reaches the center of the Warp Rift the very next turn. She has a willpower of 17, with a Force Sword for +3 with two charges and a hand full of Power cards. First two battles, she beats Kairos without needing either the Force Sword or a Power card, then uses her Force Sword in the third battle, which sees Kairos at his strongest, 17 willpower as well, but a poor roll allows the Canoness to defeat him using a Power card worth three. Fourth and final battle, Kairos is only a 16, against the Canoness's 20 with the Force Sword, and after failing to have his die explode, Kairos is quickly put down with a Power card of six, another win for the Canoness."
Basically, Ambush to deny him a roll and double X Power card for your highest value = profit.