Simply waste all opponents in a race to win this achievement. You'll do this better with the Red Eagle rather than the Yellow Hawk. If you're having trouble, try an easier difficulty level, and remember that there are several useful powerups scattered around, so explore a bit, and when you find a good tool to help waste your opponents, make your way to them and let them have it.
Given that the Pedestrian Respawn is not present in this version, it cannot be used to make the task easier. However, all pedestrians are killable in this version, as opposed to in the original game.  In addition, all levels have a Pedestrians Shown on Map pickup somewhere, which will make your job a lot easier.  Finally, if you beat the game and use Stella's car, the built-in Pedestrian Electro-bastard Ray will make things even easier.
Hot Rod and other powerups can be used to obtain this. Pick a fast vehicle, find a long stretch-way, a helpful powerup, and floor it! Maybe you'll want to waste a couple of opponents first so they don't get in your way.
It's best to go for this achievement after the game has been completed. Fully upgrade your Offensive, pick a very powerful vehicle like the Suppressor, and if you want to be sure, find a Solid Granite Car or Acme Damage Magnifier powerup, seeing as these don't block the achievement from being obtained. Then, find a weak opponent like the Razorbill, and smash it with all your might.
Kill a ped by hitting it with something other than your car
Find a place with several pushable objects, and try to drag those with you as you drive. Solid Granite Car will help you drag them without being dragged down yourself, whereas Pedestrians Glued to the Ground will help you make sure those peds stay in their place until you slowly get them with the object you're pushing. An example of a good place to get this achievement is on the Southern part of the Easternmost straightway in Mist Me!, where there are a few parked cars and some pedestrians.
In order to obtain this achievement, you'll need a YouTube account. Have something of interest happen in a race, and then enter the Action Replay screen. On the right-side bar, open the editing options, trim your clip, and save it. On the main menu, go to the Video Manager, and upload it from there. That's it. But seeing as you are uploading content, which does take its time, and could be a bit of a burden on YouTube and your bandwidth, make sure that you do something that's particularly interesting to see. Nobody likes to go to YouTube to search for interesting Carmageddon videos only to find a poor 3-second clip of a single ped being run down just for an achievement that's worth 5 points.
You can't use Stella Stunna's Electric Blue for this achievement.
In Maim Street, there's a Pedestrian electro-bastard ray in the football stadium on the right corner of the Northern side. Try to enter without scaring or hurting anyone. After getting the powerup, kill all the player pedestrians you can catch and then go for the street pedestrians before the time runs out.
Seeing as you start on Rank 99, when you win a race (hence, when you obtain Popped Yer Cherry) you'll be given this. You always drop down at least one rank when you win, so you'll be in Rank 98- after completing the first race.
Collect each of the Powerups in the game at least once
This is obtained once you collect at least one of every powerup, not pickup. In other words, you don't need to hunt down every barrel in every level. These powerups include the credits and time bonus powerups, but not the 4 "Random Selection" ones.
Only the finishing blow needs to be dealt with a mine. As such, it's advised to lower the opponents' health with care, until they're nearly wasted, then have a mine deal the final strike. Remember not to be too rough: strike them too hard and you might waste them. Also try not to deal the starting damage with mines - they're scarce. There are several mines on the Frosty Pass Ski Resort and the Devil's Canyon Mining Town.
Keep in mind that you won't always be rewarded with this achievement, just use trial and error and hope for the best!
Finish all races with each of the three win conditions
Read the guides on Wasted 'Em, Lap Dance, I'm So Ronery and Threesome. Remember to, above all, be patient. There is no rough repercussion for losing, and once a method is checked, you won't need to do it again, so just keep going forward until you've got them all!