First of all approaches are tricky against Falco. After playing against one every day for almost a year now, you learn a few things.
First of all, use the dash attack SPARINGLY, it will often be shielded into a grab combo or straight into a pillar shine combo. What you are going to want to do is maneuver around them charging up your needles and working spacing and power-shielding their lasers. Once you have a good amount of needles you can needle storm to a grab or down smash.
Once you have them down on the ground from your attack, tech chase/punish them. Find their tech pattern and take advantage of it. Make sure to change up your approaches to it so that you yourself do not become predictable. If you do you are going to get pillar shined for your moneys worth. If you do get pillared and shined make sure to DI away and tech away. Don't let them get that easy 70% on you, make them pay.
If you are playing correctly they should be dead at no more than 80%, while you yourself(assuming you can tech, double sticky tech correctly) should live to about 190%. Master the power shield timing for their pillar and laser, it will make their approaches a lot harder to time. Mix up power shielding with not power shielding to throw them off. Playing Sheik against Falco is a lot of focus on strategy combined with a sufficient understanding of how Falco moves, and the timing of his moves.
These are some of the basic things you should know in order to defeat a Falco player. Sorry I'm not know, and therefore lack credibility, but I hope you find some of my advice helpful.