Kemp followed up her opening round of 69 with a four-under 68 at Dundonald Links on Friday to move to seven under for the tournament as she briefly shared the clubhouse lead at seven under with the sport's latest major winner, Evian champion Celine Boutier, after the morning wave.
But overnight leader Shibuno then emerged to take further control, following up her eight-under 64 on Thursday by collecting five birdies after her first bogey of the event when she three-putted on the first green.
Shibuno, who hasn't not won an event since 2021, is on a 12-under total of 132, with her nearest pursuer two shots back being Sweden's Maja Stark, who recorded eight birdies -- including five in a row between the 12th and 16th holes - in her 65.
Kemp is still in the hunt, though, after recording six birdies herself, as well as two bogeys, in her second round on Friday morning.
"Pretty sure I hit a lot of greens, and I definitely holed some putts," said Kemp.
"So I was joking with my caddie, the longest putt I holed last week I think was, like, 15 or 16 feet, and today I holed a 24-footer, so pretty happy with that.
"Just nice and solid, putted really well."
The 37-year-old NSW golfer, a 13-time WPGA Tour of Australasia winner, reeled off three birdies in a row from the 12th, while Frenchwoman Boutier also shot a 68 at the Ayrshire seaside course.
Minjee Lee had earlier showed her champion's spirit by following up her dismal opening round of 80 with a second-round 66, which was enough for her to make the cut by a stroke as she prepares for next week's Women's British Open at Walton Heath.
After starting with another bogey, Australia's two-time major winner Lee rebounded with seven birdies in her six-under round and is tied for 53rd at halfway.
Sydney's rising Steph Kyriacou also made it to the weekend, shooting an excellent five-under 67, which would have been even better but for a double bogey at the 16th, to sit at one under for the tournament in joint-30th place.
