Here's an explanation on how I beat Green Hill Act 1 on Sonic Generations in under 1 minute. Beating this level in under 1 minute satisfies the Greased Lighting Achievement/Trophy. The video depicts me playing on the PC version, and while I can confirm this method works on the 360 version as well, I have not played the PS3 version so I can only assume that it's exactly the same (why wouldn't it be?). The video also lags a lot so beware of that too. This is a sure-fire way of beating the level in under a minute. There are certainly other ways that you can experiment with but this one is just to get you passed the goal in the necessary time.
-Greased Lightning Achievement/Trophy (10G/Bronze)
-As soon as the level begins, hold the spin dash (instant - X on 360, Square on PS3, A on PC) for half a second or so and let go. Keep going until Sonic stops and when he does, spin dash again until you hit a ramp. (Note: If Sonic continues to roll in a ball even after losing speed, simply jump and as soon as you land spin dash to the ramp.)
-Run forward until you get to the middle of the rosebush in the background. When you do, jump while still holding forward. You'll hit the Crabmeat, and if done right you'll continue on to hit another Crabmeat and then a Buzz Bomber until you finally end up on the high-ground. (Note: while bouncing on the enemies make sure to hold forward)
-When you land from hitting the Buzz Bomber, spin dash through the loop, and get ejected by the spring. When you land from the spring, Spin dash again into another spring that will bounce you off onto another stretch of land.
-As soon as you land, Spin dash but as soon as you hit the Check Point, jump, and with you momentum you should land and higher patch of land. Keeping the momentum, jump again and you should make it to a bridge. (Note: the grassy area and the edge of the bridge will collapse if you do not hurry causing you pursue the lower and much more slower route)
-Spin dash from the bridge and in one boost you should be able to make it through a spiral and roll into a tunnel slide (which boosts your speed once again)
-After the tunnel slide, you will be launched onto a crumbling grassy platform. As soon as you land jump onto the next platform, and then jump onto the yellow spring which will send you up to a wooden bridge.
-Spin dash here and you will be launched in the air. You should automatically hit a Buzz Bomber and land safely onto ledge where you will continue through a loop and spiral down a small rocky peak.
-As soon as you hit the check point, Spin Dash and you'll end up rolling into a series of springs that will eject you upward. It's very important that you land and the tiny area of land before the Buzz Bomber, so try to slow down your speed in the air to adjust your fall. From this area, jump on the Buzz Bomber and bounce off of it and onto a spring that will send you up onto a grassy stretch of land.
- As soon as you land, Spin dash then jump and you'll be propelled through the air onto piece of land, hit the spring and you'll end up safe ground again. (Note: This is the trickiest part of the level. If the you jump too soon or too late after the Spin Dash, you'll end up falling down into the slower route costing you precious time.)
-When you land, Spin Dash through two loops. Right after the second loop, Spin Dash through the spiral. As soon as the spiral ends, Spin Dash again and make it through the goal!