Novadrome

To be blunt, this achievement is pure luck.

Beacon Blast requires you to drive through checkpoints to gain points (or you could kill people, but yeah). This achievement requires that you drive through 7 beacons in a row in Arcade Challenge. A Beacon Blast game in Arcade Challenge hosts only 20 beacons.
Getting 7 of them in a row isn't easy. The maps do not feature a set spawning pattern for any of the beacons. You will find yourself getting a few in a row but then suddenly, one spawns right in the path of an enemy or far out of your driving capabilities.

The level you play on will play a part in the difficulty of this achievement. Something I noticed is that if I played on a more "open" map, I would almost never get multiple beacons in a row. Selecting a map that has a decent number of hazards can prove beneficial since it isn't uncommon to see the AI bunch together in one spot, stuck in a trap.
The map I used was the first map selected once starting up the game. Now, vehicle selection. I do not have many vehicles unlocked but I found it easier to play as a car with lower stats. I had a harder time trying to get multiple beacons than I did with the first car at the selection screen. I don't know why that is (especially since I was using a car that was equal or better than the first car). Part of it is because when using a better vehicle, the enemies tend to have better vehicles as well.

As I mentioned earlier, this achievement is unlocked through luck. The game will have to spawn 7 beacons in a row that are either close to one another or one an easy-to-follow path. If you fail, the only thing you can do is try and try again.