The engine ought to be capable of that, but the bit you are going to need to spend the big bucks on will the ‘everything else’
A standard manual gearbox won’t cope with that power. The reason all the YRV Turbos are auto is because no Daihatsu gearboxes would tolerate the torque that the 130bhp K3-VET puts out. You’re aiming for a 50% increase in that power/torque so you’ll blow up gearboxes left right and centre.
There is a solution, but its a £3k (minimum) Compact Motorsport gearset, plus fitting & installation.
Then there is the brakes. I have a notionally 110bhp Sirion Rally 2 and the brakes are barely adequate if I’m honest. Again, you’re going to have 80% more power/torque than I have on tap, and at a much lower RPM therefore more usable. You will need to upgrade the brakes quite substantially, not sure on cost but budget for a grand at least for parts + install. I believe that you can modify MX5 brakes to fit, but its not a simple process. You might need bigger wheels & tyres to clear bigger brakes too if you’re not already running 15" wheels.
With that much power on tap you’d be wise to fit some chassis bracing, Ultra Racing have some good stuff but you’d be looking at £500+ for a comprehensive setup. And quite possibly improved suspension setup too, some adjustable coilovers from a decent outfit will probably be another grand S&F?
So just to set the scene, thats £6k+ before you spend a penny on the engine. All do-able, and largely off-the-shelf, but for that much money you could just go out and buy a 200bhp 2 seater soft top thats ready to go.
I’ve said it before, and will say it again, play to the Daihatsu’s strengths. Its light and nimble, make it HANDLE and you’ll have a far more enjoyable car even with standard engine and gearbox. For <£1k you could get a full set of chassis braces, polybush the standard suspension, upgrade the ARBs and fit a set of semi-slick tyres to the standard wheels and you’ll out-handle cars costing ten times that much. It’ll also drive nicely on the street.
I don’t mean to pour cold water on your ideas, but you should consider the big picture. If you want big power then starting with a Daihatsu isn’t the way to go. If you want a car that will out-handle a lot of other cars then its an excellent starting place.