しっかりする(shikkari suru) means to hold steady, be level-headed. ほっといて（くれ）(hotto ite (kure)) (note that it's ite, not itte) means "back off," "leave me alone." For example, if you have met with some adversity, someone can say "shikkari shite!" (as in "hold your head high"); and if you're busy and someone is nagging you, you can say "hotto ite."

I leave just some follow-on to that nice answer; ほっといて is for women. ほっといてくれ is for men. The root of this verb is "ほっとく" But this expression is casual. More formal one is "(私のことは)ほうっておいて・ほうっておいてくれ"the root:ほうっておく