Build a swarm of LRM's and light carriers and go for his labs and frig constructors...ignore everything else. Go after them fast and hard. Jump from system to system with your scouts on auto to keep you apprised of where he's building them.
This will have a twofold effect. First, he'll be expending massive resources trying to rebuild labs and on the kodiaks themselves...they aren't cheap. They'll also take a long time to build, compartively. This allows for the secondary effect...usually an abandoning of the rush.
You're flying in fast LRM's and light carriers, so you can ususally use your bombers and LRM's to take out his labs and frig yards before he has a chance to counter. While doing that, you can have a forward frig yard or two replenishing the few losses you take while leaving you ample resources to work on your main strat.
The benefit of having a large fleet of LRM's and light carriers is seen at the choke points./.. even if he's got a large fleet too, and even if he's got a PJI, you can take that out fast and jump out while on the run and have minimal losses, leaving your harassment fleet with enough numbers to do damage in his back yard.
The key is ignore everything but your target. If he's working towards an HC rush, chances are his fleet size is minimal and his static defenses aren't much better simply due to the overall resource and credit cost of trying to HC rush. If it's specifically a Kodiak rush, he's likely got Trade osts up....likely multiples. If you have the time and/or are not opposed at that planet, make those secondary targets. Destroy his economy and he'll have no choice but to at least temporarily abandon his tactic...while you've already had the chance to build on yours while he's been trying to fend you off.
It's all part of the hit fast, hit early, and hit often tactic. But with this one, you're trying to get to his back yard and take out his support system, ignoring his border fleets and heavily defended positions where he likely doesn't have his HC rush infrastructure.
YMMV, of course...