Lot's wrong. It's mainly fantasy, like the Mars Trilogy but speeded up even more and more fudging of the numbers.

1. Nuclear weapons are nowhere near powerful enough. You'd need hundreds of thousands of explosions of the largest nuclear bomb ever made probably, the Russian Tsar Bomba, millions of them. And even if you could do it, the radioactive fallout would be huge.
2. We don't know if there is enough CO2 there. We know of enough to double the atmospheric pressure. It's not clear whether there is enough to get to ten times the current levels of CO2 as you need to push Mars into a runaway greenhouse state. (And if there is, why is it not already in that runaway state since it's had times in the geologically recent past when its ice caps almost vanished?).
3. I've no idea what it means by a "CO2 machine" and it doesn't explain. Unless someone explains, I'll assume it is just made up. You could make machines that mine carbonate rocks on the Mars surface and heats it to high temperatures to release the CO2, like the process used to make cement from limestone, but that seems unlikely, and not sure what else they would be. If anyone knows do say!
4. Orbital mirrors would need to be huge, similar in size to the planet itself - you want to double the amount of sunlight reaching Mars.
5. If you used life to create oxygen on Mars, it has to make it from the CO2 taking carbon out of the atmosphere, enough to cover the surface to a depth of some meters with organics - which would take perhaps 100,000 years in an estimate by Chris McKay
6. There probably is not enough water either - remember that the equator is bone dry desert to great depth. There's lots of water trapped in the ice at the poles, but it would be like pouring water into the Sahara.
7. CO2 is poisonous to humans so we couldn't breathe the air even if they did make enough oxygen - so you need something else, such as nitrogen, as a buffer gas and remove just about all the CO2 from the atmosphere.
8. You need to keep the planet warm after terraforming. An Earth atmosphere is not warm enough for Mars at twice the distance.

There are genuine proposals to terraform Mars, especially the Mars society proposes to do it - they suggest around a thousand years to get as far as a CO2 atmosphere with trees only, no animals. But there are also lots of potential issues with the idea too.

This is pro terraforming, and more accurately describes how they think of it:

The Big Idea - Making Mars the New Earth - National Geographic Magazine

I'm very sceptical of it myself though as something we could really do. It is great fun as an intellectual idea to explore.

SOME OF THE PROBLEMS FOR TERRAFORMING GENERALLY

It is not at all clear that we can terraform Mars, and if it is possible, with current technology, it’s a thousands of years, or perhaps a 100,000 year megatechnology project. There are so many questions. How sure can we be that we will continue such a project, when it is likely to cost billions of dollars a year and need support from Earth for thousands of years?

The Mars trilogy is science fiction and the optimistic real world estimate from the Mars Society takes a thousand years to a stage where trees can grow but no animals or birds yet, and humans need aqualung like closed system breathing kits to get around. And is based on assumptions about the amount of dry ice on Mars which are not yet confirmed, and doubts have been cast about how much dry ice still remains there.

Do we have the scientific understanding needed for it? We have never terraformed a planet, and with all our technology on Earth, we find it hard to just keep the CO2 levels on Earth from rising by tens of parts per million. Would it unterraform as easily as it terraformed or go to some undesirable end state. Is it possible at all?

What about accidental planet transformations, where lifeforms we didn’t mean to introduce change the climate in unexpected ways? And Mars gets much less light than Earth, so an Earth atmosphere would not be warm enough for Mars without planet scale thin film mirrors to double the amount of light reaching Mars, or industrial levels of production of artificial greenhouse gases (200 half gigawatt nuclear power stations to supply power, and 11 kilometers of fluorite ore mined per century to make the gases).

Are we confident that this is what our descendants a thousand years from now will want us to do for them? Will they be pleased that we started the project so soon and made Mars just as they wanted it, or will they be frustrated by our failed projects, and lament the pristine Mars they would wish to be able to study and possibly transform for themselves?

Trouble With Terraforming Mars

Imagined Colours Of Future Mars - What Happens If We Treat A Planet As A Giant Petri Dish?

To Terraform Mars with Present Technology - Far into Realms of Magical Thinking - Opinion Piece

Why Nukes Can’t Terraform Mars - Pack Less Punch Than A Comet Collision
Our Ethical Responsibilities To Baby Terraformed Worlds - Like Parents
How Valuable is Pristine Mars for Humanity - Opinion Piece?