Hosmer went 3-for-4 Sunday against Kershaw, including a two-run home run, his 12th, in the Royals' 5-2 loss on Sunday.
"He's tough," Royals manager Ned Yost said of Kershaw. "We couldn't do much on him. I mean, [Hosmer) had an awesome day with three hits. He had a great day off him. He's good, he's tough. He's tough against right-handers, as tough as he is against left-handers."
Hosmer now is 5-for-8 lifetime against Kershaw.
"We faced him maybe a couple years back in Kansas City, not that he's changed arsenal or changed his game," Hosmer said. "But you know it's going to be a tough game and you know it's going to be a tough at-bat, and I think that's what makes him so good is that he holds guys on. He fields his position well, there's no real way you can kind of sneak some runs behind him."
Hosmer's home run in the fourth cut the Dodgers' lead to 4-2, and just barely cleared the wall in left-center.
"I was hoping it made it, that's why I was watching it the whole way," Hosmer said. "At first, I thought [center fielder Trayce Thompson] made a good catch out there. I already had one taken away from me this year, so not trying to see that again, so I was happy to see the ball roll around outside the fence.
"Stay on his pitches. The approach for me was to be ready to swing early, especially if he fell behind in the count. You don't know what pitch it can be, but you know it's going to be in the strike zone so you really gotta stay aggressive."
Hosmer finished the first half with a .318 average with 12 home runs and 42 RBIs.
"A lot to look forward to," Hosmer said. "I think overall, we like how we bounce things back, we still feel that, obviously, we could have played better in April. All in all, it was a decent first half for us, and we go out and watch Moose [Mike Moustakas] hit some homers, take a couple days off and try to get back in rolling the second half, and get to where we need to be.
"It's definitely a good feeling. We were playing the worst baseball we played and things didn't look good as a whole. And for us to put us in this situation now at the break, and pretty much everybody healthy, I think we like where we're at."