When it's night time. Go to living room first and click "Chat" button. It will automatically open the path for you. Hope this helps.
Edit: I reread your sentence. So you'll also need at least 20k or 50k cash I think and you have to go outside and do some running at night time. Keep running until you reach the end. DON'T END the run.
If you don't have enough stamina then keep on running, fighting for cash and do recording and purchase coin converter: Points = Coins. More points multiplier = more cash/coins. Get points from recording and accepting viewers request.
Buy energy drinks and upgrades. Do this first then chat with her when you buy the running shoes from the Kat girl merchant at Night Day. Sorry for long paragraphs.