A guide to completing World 2-1 in Super Mario Bros 1 for the Nintendo Entertainment System.
Explore World 2-1
Go to the right, and you'll see three bricks above you. Hit the middle one to get a Mushroom or Fire Flower. Then go up the stairs on the right, but be careful of the Goomba there. Fall off on the right side of the stairs, and if you are Fire Mario, hit the Koopa Troopas with fireballs. Otherwise, you'll have to be careful about hitting the Koopa Troopas, because if you kick their shells, one of the shells will keep bouncing back and forth. If you can manage to jump on the bouncing shell again, you'll stop it from moving.
Stand to the left of the left side of the bricks above you, and jump straight up. You'll reveal a hidden block that contains a coin. Jump on top of that block, then jump straight up again. If you collected most of the coins in World 1-3 without dying, or if you warped to 2-1 via Warp Zone, you will hit an invisible brick and a 1UP Mushroom will come out. Otherwise, if you didn't get most of the coins, or you died in World 1-3, there won't be a 1UP Mushroom there.
Jump over the blocks on the right, then get rid of the two Goombas. There is a Piranha Plant in the pipe on the right. If you're Fire Mario, you can get rid of it with a fireball. Otherwise, stand next to the pipe and wait for the plant to go back down, and then you can safely jump on the pipe and go to the right.
Up ahead, hit the bottom left ?-mark to get a Mushroom or Flower. You can hit the other ?-mark blocks if you wish. The green Koopa Troopa will fall off of the blocks when it reaches the edge, so make sure not to let it fall on you. You can try to stomp on it and kick its shell through the other enemies up ahead.
As you go to the right, there is another Koopa Troopa and some Goombas. Don't hit the brick that is floating by itself. Instead, jump on it, then hit the leftmost brick above you to make a Starman come out. Collect it, then while you're flashing you can go to the right and let the Goombas walk into you while you hit the four ?-mark blocks on the left and the three on the right. Before you move on, if you want a lot of coins and don't mind skipping part of this level, jump onto the group of four blocks on the left, and stand on the rightmost one. Jump up to hit the brick just to the right of the block you're standing on. This should make a vine grow up into the sky. Jump up to where the vine is, and touch the vine to get onto it, then press up to climb up.
Option 1: Ignore the Vine
If you didn't climb the vine, you can go to the right, jump over the pit, get rid of the Goomba that falls down from the pipe, then stand next to the pipe or use a fireball to get rid of the Piranha Plant if you're Fire Mario. When the Piranha Plant is gone, jump on top of the pipe and press down to go down into a secret area (there's no reason to ignore this pipe, because you won't miss anything by going down below). Get the coins in the underground area, then go to the right and enter the pipe. You'll come up a pipe that is a short distance to the right of the one you went in.
Go to the right and stomp the Goomba or hit it with a fireball if you're Fire Mario, then stand next to the pipe on the right, or hit the Piranha Plant with a fireball if you can. Jump on top of the pipe when it's safe, then go to the right and get on the short pipe when it's safe. Hit the leftmost brick to make a Mushroom or Fire Flower come out. If it's a Mushroom, wait for the Piranha Plant on the right to go down, then jump from the short pipe to the one on the right before the Mushroom can get away.
Go to the right and get past the Koopa Troopa, then hold B and make a running jump over the gap on the right. Farther to the right, there is a green Koopa Paratroopa. Get past it, then make a running jump to get over the pillar of blocks. Then skip to Part 2 below.
Option 2: Climb the Vine
If you did climb the vine, go to the right and jump onto the platform that looks like a string of pearls. It will start moving to the right. Jump up and down to try to collect all of the coins above the moving platform. If you fall off of the moving platform, you won't be able to reach most of the coins. If you're still on the moving platform, it will go past three coins down below. Try to fall through those coins. If you lost the moving platform, just go to the right and make a running jump to the right, and you should go through some or all of those three coins.
Part 2
Hit the bottom-left brick to get some coins. Then go to the right and hit the ?-mark block. The brick above it contains a Fire Flower or Mushroom, but it can be difficult to reach. You have to stand to the left of the lower block and jump on the lower block, then quickly crouch (if you're tall) and jump up to hit the upper block.
Go to the right and either stand next to the pipe or hit the Piranha Plant with a fireball if you can. Go to the right when the plant is out of the way, and ignore the green Koopa Troopa if you don't want to deal with its shell bouncing back and forth. Jump on top of the two bricks, stand on top of the rightmost brick, and jump straight up to reveal a hidden block.
Then you can either jump on top of the block you revealed, or you can jump onto the spring to get to the top of the tall pillar of blocks. If you jump on the spring, you need to press the jump button when the spring is fully compressed. This will make you jump very high up so you can get on top of the pillar of blocks.
From there, run and jump to the right to reach the Goal Pole and move on to World 2-2.