Well, as the achievement says, you need to get a perfect 5 stars on every level. This is a time consuming and fairly difficult achievement - especially because the game instructions are very poor, and leave out a lot of non-obvious tricks. But I can help with that. :)
1) SCORE DOES NOT APPEAR TO MATTER. The loading tip lies! The 5-star ranking is based off of time. In particular, this means you never need to kill enemies that are out of your way, and you do NOT need to collect the B U R G E R letters. (Some levels are a joke to 5-star if you ignore B U R G E R!) I wish I'd known this going through America and Mexico. :)
2) The only thing that really matters when it comes to time is running over the burger's top bun. Other ingredients will be knocked down automatically and can be ignored.
3) A key mechanic (which I guess is clear if you played the original BurgerTime; I had not) is that any enemy standing on the top bun before you drop it will automatically drop it an extra level. You can do this by having them follow you onto it, but it's almost always easier to stun them with pepper while they're on it, then drop it as normal. (You can walk through stunned enemies.) This works for all enemies, including Haba De Niro (though you have to do it before he explodes). It's usually worth it to wait a second or two for an enemy.
4) The bonus drops from enemies stack, so it's especially worth it, if you have multiple enemies on your trail, to stun one on the top bun, wait for more to arrive, stun them, and then drop it. (Sometimes you can complete a tough burger with a single drop this way!) Pepper is plentiful in most levels; don't worry about rationing it.
5) Even for enemies that don't normally walk over the bun, you can pepper them, pick them up, and then run onto the bun; that counts as if the enemy was standing on it! This trick is essential for 5-starring the America boss (you can grab Pickles and complete the burger in 2 drops instead of 4). Note that picking up enemies is completely useless except for this. Also note that you can do this with Haba De Niro; he takes longer to explode while you're carrying him.
6) Powerups always appear in the same spot, but whether they're there at a given time is random. On some levels you'll want to keep restarting until a particular powerup is near - especially for Rockets, since they're so useful for skipping sections of levels. (Soda is also an extremely useful powerup - not only are you much faster, but you're invincible too!)
7) While climbing or descending ladders, you'll pepper upwards or downwards! It took me a long time to notice this VERY useful feature. There's rarely any reason you have to go around enemies; just pepper then run or climb through them. (Be a little cautious, though, since the game's not very well programmed and pepper can be unreliable. I'd say most of my restarts were because of pepper fails.)
8) Don't be shy about dying on purpose to respawn at a checkpoint (those little purple arrows). You don't need to do 5 stars and no deaths on the same run. :) This is very helpful on a few levels; you can complete a burger and then die to respawn near the top again.
With these tricks in hand, most levels will fall in a few attempts if you just learn the layout, think about the fastest approach, and restart whenever you mess up. If you're struggling, there's probably a better route. On some levels it's better to focus on one burger at a time; on others it's better to run across all the difficult-to-reach top layers first, then focus on individual burgers; and sometimes you'll just want to complete 2-3 burgers in parallel on the way down. You can save a ton of time on certain levels by using bonus enemy drops to avoid difficult-to-reach layers. And abusing the Rocket often lets you bypass time-consuming sections of the level.
So, good luck! And don't be too intimidated. If you're decent at platformers, the achievement is well within reach - as long as you have the patience to keep retrying levels and tolerance for the game's somewhat crappy controls. :)