Kai's first campaign level is a good stage to attempt this, as your CPU opponents are all fairly weak. Bring draw cards like Passionate Research and Nice Present to assure you can get a hyper or two, maybe some attack buffing cards to bring down the tankier Marie Poppo, and from there attack anyone at any chance you get. Ensure any kills made are under the effects of Cast Off, as otherwise they do not accumulate towards the achievement total. Boss and battle tile kills also do not count. The 5 kills do not have to be made using a single hyper, but you should still maximize as many kills as you can per hyper.