Hotshot Racing

The wording to this one is a little bit confusing. You need to make sure that not only you directly or indirectly destroy 3 cars in the span of 10 seconds, but that those 3 cars have never been hit by your car before that 10 second interval! Needless to say, that if you keep playing this mode normally, you drive as fast as you can, you will bump a lot, and since the first lap or two are easy to survive for human players and AI alike, you'd be hard pressed to do this naturally. Congrats if you did, but it requires a lot of luck - or, alternatively, careful planning. I identified two ideal solutions to pull it off, based on whether you have enough controllers or online buddies or playing solo.

1) Super-easy solution, requires 4 controllers or 3 buddies online:
Whether you're playing locally in split-screen with 4 players or by finding 3 other folks who want to get this achievement with you, the execution never changes. All human players stand still at the start, doing absolutely nothing. You can make sure to get closer to each other to make things easier, as long as you make sure there's no touching. As soon as the lead AI hits the first checkpoint, a 10 second countdown begins. When it hits 6 or so, make sure you touch all 3 cars slightly. All players will be destroyed in the span of 10 seconds by the timebomb. Achievement unlocked with little to no effort.

2) Medium difficulty solution for solo players:
Single Race, Jungle, Temple Ruins. Drive Or Explode, Expert, 7 laps. With this combination of difficulty and track, AI will be pushing and shoving each other a lot, causing many of them to go into red health as early as lap 1 or 2. Follow the pack from a safe distance, making sure you're always either last or that you have at least 3-4 cars ahead, and of course that you're never touching any other car. You will see drivers go low on health continously, but make sure you don't make a move if you're close to the finish line, which replenishes 35 health to all racers. When you see 3 cars that are on fire and with red health, hit them all in the span of 10 seconds, between the hits, the close walls, the speed loss and the other cars coming up there's good chances of them getting destroyed in a matter of seconds. It requires luck, because sometimes there's only 1 or 2 cars at a time go red on health. If you have even a single person helping you locally or online, you can make this one easier by having two players ram into merely 2 AIs, with then the second player going straight into a wall for an instadeath, after making sure you touched the car obviously. It still requires luck, but it just became notably easier. I'm reading people claim your own car counts towards the 3 counted for the achievement, but I don't believe this is the case, as I did not unlock the achievement destroying 2 cars and myself in 7-8 seconds.

A bit of a confusing achievement that requires you to play in an unnatural way, but it can be cheesed.

One major point that I'd like to make clear for everyone is that your vehicle can count as one of the three vehicles. I connected a second controller and was playing against a friend. We ganged up on one vehicle to the point that they had low health and then I finished the the AI and his vehicle off. Within a few seconds of staying still my vehicle exploded and the achievement popped. This might be more of a tip than a solution but just understand that your vehicle can count as one of the three.

Here's how it unlocked for me: 3p online on surf city with 2 extra controller's. (I was going for the K.O. achievement but ended up getting both)

All I did was let the cars hit the wall, as they will, and turned around to hit the one with the lowest health bar first. Hit both cars and proceeded to hit the wall myself to finish the race faster. When I exploded the cheevo popped. I guess your car counts as well.

Hope it can help you guys!

This is the solo method for people without extra controllers.

First of all, in the descriptions of other guides I think people are reading this achievement wrongly or the achievement itself could have been worded better. I believe this doesn't mean you have to kill them all within 10 seconds, but 3 cars have to die within 10 seconds of you hitting with them in one race, which is why it's best to put 7 laps. Plus the earlier laps of longer races on Drive or Explode your cars go slower and the speed increase is more gradual making it easier.

You need to set up a race on Expert difficulty on Drive or Explode for 7 laps, I found Temple Drive to be a good track. Also pick a car you're good with, but I recommend the Super F-90 because it handles well and it's fast.

This is hard to get so you may not get it first try so keep at it. The best tips I can give (which I do explain in the video below), is try and take one out straight away. In the video I didn't get one I was aiming for at the start, but sometimes I will kill one just after the first corner, if I didn't I would just restart, but in the case of when I got this achievement I didn't restart and was fortunate and clever in the way I got it. The other tip I can give is if you see one spin just smash into them, there's a chance they will die within 10 seconds.

I explain things in the video which will help, but it's still a hard achievement.

As I said at the start, there is a method where you need at least 2 extra controllers, having 3 extra may help more but this is for people who don't have enough extra controllers.

I really hope this helps you, good luck!