This is a solution for Gold Medal Winner, but the tips and techniques apply here.
There are 48 races in total and the breakdown is as follows:
Easy: Races 1-10
Medium: Races 11-30
Hard: Races 31-48
You unlock the medium races after medaling appxroimately 8 easy races and the hard races unlock after medalling all easy races and medalling approximately 14-18 medium races (This needs clarification, but this is when they unlocked for me on both the red and black suited spiderman).
This is a few tips I posted on a thread in another forum.
There is no difference in terms of speed/balance between suits, only combat differences, which is not required for races. So it does not matter which suit you use.
Many people say always use the mega web zip to go from checkpoint to checkpoint, I find that this can be very inaccurate to get into checkpoints and should only be used when checkpoints are more then 80m away. For checkpoints which are closer together I tapped LT twice to make me web a little faster and more accurately get to into the checkpoint. Start off just trying to gold all the easy races, races 1-7 are really easy, races 8-10 are a little more challenging. These races are simple and only utilise fast web zipping between checkpoints and landing.
Once you have done these you should have mastered the basics of webbing really fast from checkpoint to checkpoint. Then start work on the medium races, races 11-21 are not that hard to gold with a little practice, races 22-30 are far more challenging in general.
The medium races bring in more tricks into the races such as: wall running, wall crawling and wall jumping. Races that require wall running here is a neat trick: to keep momentum hold LT and with your fingers hold A and B and move up the wall (I it is much easier to do this with fingers rather than your thumb). As you run up the wall keep hold of LT and B while pushing forward with your left joystick, then let go of the A button. This will cause you to jump up the wall. Once you are back on the wall, hold the A button again and keep repeating. This will not only stop you losing momentum on wall running, but also allow you to wall run much faster. If a wall jump is required press the A button as usual, but then let go of the B just afterwards. This will jump you off the wall and stop you going back off the wall.
Wall crawling is a simple technique. Make sure you press B at the wall first before holding LT. This will put you into a wall crawl, once you are in a wall crawl, hold LT and move ith the joystick to crawl faster. Also jumping by pressing A up the wall allows you to scale buildings even faster (same as wall running).
Race 24 is really hard, you will have to perfect web zipping through the park without any mistakes, it will take a long time so you will have to be persistent. The hardest medium race is race 28 it was the third to last race I got on gold and was really annoying, to get gold you have to get 45 secs (I once got 45.008, I was not very happy) I would leave this to one of the last races you do. The best tip I can give for this race is when you need to get on top of the buildings really quickly, while doing a normal web swing hold LT to make you go faster and hold A, then when you get near the building let go of A this will make you jump really high in the air to get on top of the building, this will save you about 4 secs of time as you don't have to wall run or wall crawl up the buildings.
Then you have 18 hard races to do, not much I can do here to give you any help except tell you to practice, a lot. Its best to start with the easier races first and work up to the harder ones. The easier races are definitely race 31, 36, 37 and 48 so try these first and whatever you do leave these races to last 32, 33, 39, 40, 44 and 47. These are by far the hardest races in the game, race 39 was the last race I did and was horrible.
The hard trick races have two lovely tricks called loops and orbits in some of the races, these are hard to pull off and are really time wasting, it is due to these that make race 39 the hardest race in the game by a long way. The trick to pulling of successful loops and orbits is to web as close as you can to the pole/object that you are required to loop or orbit round. This makes it easier to web to the correct object and reduces the distance of the loop/orbit, because of the shorter web. The shorter the distance that you travel whilst doing the orbit will allow you to get more speed as you release your web from the loop/orbit. Make sure you hold/tap LT whilst performing the loop/orbit to travel round faster.
Besides that I cant really offer any advice except make sure you have web swing speed 7 ( max swing speed) and make sure you practice and have a shit load of patience. Listen to some relaxing music while trying these, it helps relieve some of the stress.
Do not attempt this achievement until you have every other achievement. You will need several hours of prcactice with Spidey to be able to pull these off.
Stuck on a race? Post in the comments or send me an xbox live message for any specific questions and I will try my best to answer them as soon as possible. Happy swinging.