Snake is a very, very difficult match up.
This is what you must do:
Jab combo. It comes out faster than anything he has. Literally, EVERY SINGLE MOVE THAT HE HAS gets beaten by Lucas's jab combo.
PKF spamming doesn't work against a good snake, because there will be mines in the way. One might give the advice "just hit the mines with PKT" or "Just let them hit you, it'll open up the stage and they don't do that much damage." Don't do this. The mines are killer. You'll be at 100% before you know it, and then you're just one of snake's jab combos away from being off the edge.
No PKF means no approach, especially when snake has the 'nade that keeps you at bay. You're going to have a hard time if Snake gets away from you. You want to keep him close. Most of all, if you get on the offensive, stay on the offensive. Take control of the stage, and keep control. Keep him on the defensive, because all he has going for him at close range is his jab combo, and, as I've mentioned, yours is better.
How do you get near him for when he does slip away from you? Carefully aimed PKFs, find a position to camp where he can't 'nade you, and watch the hell out for his missile thing. If you're brave, shoot a PKT off or two. That'll scare him, if he knows what he's doing. If it doesn't scare him, even better, because you can **** him up with it. The problem is that he has more long-distance pressure techniques than you, what with 'nades and the missile.
Try to take him to a small stage. Yoshi's Island is preferable, but smashville will also work. Try to keep him from putting down his dsmash mine as much as possible, that's the real killer. For god's sake, watch where he puts his b-down mine. Keep a mental tab at all times of where that mine is, because trust me, you aren't going to be able to see it all the time.
If this snake is roll-dodge happy, then pressure his shield with nairs. A nair to ftilt will get his shield looking VERY tiny, and the knee-jerk reaction is to let up on it. If you dsmash at the right time, it will hit him, after a nair>ftilt combo. If he's at a low enough percent, he's heavy enough that it will hit him twice.
Your damage should be coming primarily from jab combos, fairs, nairs, and utilts. When you get him to a respectable damage, start being more liberal with dsmashes and fsmashes.
However, he will not die off the side until obscenely high percentages. You must ledge guard. It is extremely difficult to edge guard a Snake. I might even call it impossible to do reliably. His recovery is simply too weird. PKTs don't REALLY work, unless you can read his recovery well enough. I've tried many times to PKT a Snake out of his recovery, and you have to get the timing right, because you have to put the PKT above him. It's too difficult.
If you know when he's going to up-b, it's better to jump out there with a fair. Sure, the knock-back isn't as horizontal as you might like, but it's a start, and it'll put more pressure on him to get back.
