Well, as title suggest you have to kill spinning bastard without firing weapons.
Use of any "cold weapon" aka meal combat is allowed thought completely unnecessary and can prevent achievement.
What to do?
Just dodge it's attacks and when button for statues (pillars) goes green rise it and stand behind and let hedgie to crush it. Do it 5 times and that's it.
Just keep in mind that pillars folds down after 10s so little timing with hedgies charges is necessary.
Good luck