I gotta admit, I do have some issues with his neutral game and the overall lack of variety and effectiveness it can have, but once I've taken the neutral, I feel his moveset can be very fun and exciting. As for his tilts, down tilt is a fast combo starter at almost any percent. From 0 to about 20%, you can string it into:
-Dash attack->Up smash or Up air depending on weight and/or percent
-Standing Grab-> up throw-> Up air
or -Side tilt
Even if your opponent spot dodges, you can spam two in a row and ppl rarely expect it. Once you get the opponent over about 50%, you can then start racking up some serious damage with down tilt into upsmash or use it as the usual kill confirm once you get over 90ish%.
As for side tilt, it has great reach and decent speed. When you land a sour nair from above between about 20-50%, you can combo it into an up-angled side tilt. Other than that, results can vary with side tilt.
Now for up tilt. This is one of the most slept on tilts Greninja has in my opinion. The disjoint on that tongue is insane, able to outreach even Cloud's Dair. Its speed is good and it combos into up air and Bair all day long. If your opponent likes to short hop attack for their neutral approach, just dash underneath them and slap em with that tongue. At 0%, up tilt can combo into itself once and then you can follow up with up air. At any percent over 30, you can up tilt into up air and Bair for damage racking or even use it as a kill confirm at percents over 110%. The best thing about popping up the opponent, is that even if you miss the followup or they manage to dodge, you can start leading them with an airborne shadow sneak and fast fall to catch their landing. Their eyes are almost always on you in the air, so hitting them with this trick shot is incredibly easy and makes for a sweet surprise kill at 90% or higher.
Other than that, I'd love to hear if anyone has any other good suggestions for dealing with neutral. I personally use a lot of dash dancing to snag that first dash attack and move from there.