Pure

Stage 7 contains two freestyles, two races and one sprint. To get the achievement you must finish 1st in all five events. If you haven't already I suggest you have an atv specific to each event type (one of race, one of sprint and one for freestyle). Both the race and sprint atv's should focus on speed and handling with little recognition of tricks. While the freestyle atv should focus mainly on trick (because that's what your doing).

In the Freestyle events, make sure you focus on tricking and not your opponents or racing, I actually stop for 5 seconds at the start of the race to give myself a bit of room to move. What you want to do is build up some combo's, sometimes it's good to do a big Y or special trick and then in a previous/future jump do two/three small A jumps to hit up your multiplier to allow you for bigger benefits. If your still struggling with the freestyle events be sure to change up your routes, you might find an easier line to link up a combo with jumps. Focusing on my method of combo's combining quick A tricks and big Y and Special trick can also help you get the 'Killer Combo!' achievement (it worked for me)

In the Race events, focus on your speed and not crashing. Be careful if you want to trick and always leave yourself enough time to plant a clean landing (which allows for a speedier exit from the ramp). Use your boost on straights and make sure not to use it before tight corners as it usually has little effect. If you know you can't win the race, then restart and hope for a cleaner run. If your still struggling try different routes and learn more about the track, it helps especially in the later stages as the shortest routes aren't often the quickest.

Finally in the sprint events, focus on your acceleration and cutting the corners tight. Stuff away from the pack if you can as you'll get slowed down and avoid preloading over the 1-2 jumps in the map if you can as the longer you stay in the air, the more of a gap others on the ground gain. If your still struggling, focus on the leader as see what routes the guy is taking through turns as it'll most likely be faster then the other racers (he's infront for a reason, right?)

Finish 1st in all events in Stage 7. If you are going for the No Messing achievement, finish the world tour first and then come back to it. Completing Stage 7 also builds up for the Pure Perfection achievement which is worth 100 g's.