All of these achievements are self-explanatory, simply beat the game on any difficulty. If you get stuck use the video walkthroughs on youtube.

Enemies that you can stomp on are cockroaches, crocodiles, and rats. You can find plenty of these around the levels where you are in the Metro Station. You can also use the GLOPP Ray to revert enemies to their former state and then you can stomp on them. Stomp on them with the . Here are some guidelines to go by if you don't want to use the GLOPP gun.
Level 2-1 - 5 rats
Level 2-2 - 1 crocodiles, 3 rats
Level 2-3 - 1 crocodile (you need to kick him before he transforms)
Level 3-1 - 7 bugs (before picking up the GLOPP GUN later in the level(in case you missed the secret at the beginning of the level).
Afterward, just about every enemy is a potential stomp-fest!

It is impossible not to get this achievement in one playthrough of the game. In fact, if you kill a good amount of people on the level "Rooftop Rebellion," you will most likely unlock this.

This achievement is a lot easier than it sounds. There are a total of 240 nuke symbols across the game, that means you only need to get 5 of the 10 in each part of a level for you to get this by the end of the game. I personally unlocked this achievement half way through Level Worker Safety last. Just make sure you go in every room you can and if you know or think that you can blow a wall up with a pipebomb... DO IT! You will find secrets that usually have nuke symbols and other stuff that will help your progression. You also use the information here: Link

Most likely this is the only achievement you will not unlock in your playthrough of the game. For this simply keep replaying the level over and over again (by the way this is only part 1 of level: "Roof Top Rebellion") until you have the gist of what you have to do and what you don't have to do, and keep doing the level until you know how to speedrun it or you can watch this video.