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I'm not sure if you mean the whole floor or the bottom of the steps....
If the bottom of the steps, depending on how much you're talking about an sds and chisel set could do it. If it's deeper I'd work out a way to get a roughly even depth with an angle grinder/similar then chisel that out.
If the whole floor I reckon paying someone in one go is the way to go. You need to dispose of all the rubbish as well so I think even DIY costs will add up.
The back of our kitchen leads up some wonky concrete steps to a washing machine room. How would I go about chiseling all of that floor out so it's the same level as the kitchen. My intention for this would be so I could lower the roof of that room which would allow me to lower the decked area above it/outside to eventually have a door leading out to the garden instead of a window that I have to climb through.
How DIY-ish is the first part - I think the lowering of the roof will be beyond me but am trying to cut costs where possible.