This looks trickier than it is, it's just a case of getting the timings right. Which is what I'm going to tell you.
First you need to get to the "Spike Dodging" level. It's in the Graveyard, near the boss door at the left hand side. There is a door to the right and down a little bit from the boss door, then another door down and right a bit from that, it's that door.
Once inside, it's basically just a room with 7 levels and a small gap at slightly different points to jump up to the next one. I'm going to refer to the levels as level 0 up to level 6, where level 0 is the bottom one. Level 0 is where you start and it has nothing dangerous on it, so you're free to run about it, each of the other levels has a Spikey that rolls left and right. I will refer to the Spikeys as Spikey 1 to 6, where the number relates to the level the Spikey is on.
First, line up with the gap through to level 1 and wait for Spikey 1 to go to the right. Jump up to the left, grab the gem and back down the gap to level 0 before Spikey 1 comes back.
This time wait for Spikey 1 to go to the left and then jump up to the right, grab 2 gems and up the gap to level 2 before Spikey 1 comes.
Getting up the gaps is what will trip you up the most, it's easy to misjudge a gap and then fall back down and be hit by a Spikey. I think the key is to not rush it too much. Obviously you need to be fairly quick but you have more time than you think. Use that time to line up with the gap before you jump. Don't just try and frantically jump loads of times when you are near the gap.
Now you are on level 2, but you can't hang around because Spikey 2 is coming. Wait for Spikey 1 to pass back to the left below you and fall back down the gap.
Note that you could do this jumping up and down the gap, dodging the Spikeys, for as long as you like. The timing stays the same. You might want to do this the first few times when getting your bearings but I recommend not hanging about too long, it only gives more time to make a slip up.
Another tip is that when you fall down a gap that you are planning on jumping back up, stay exactly where you are when you land. Don't move about on the level below. That way you know for sure that when you jump up you won't miss the gap.
Now wait until Spikey 2 goes to the right and jump up to the left. It doesn't look like there is much room to the right, so you might think that Spikey 2 would get you quickly. But the Spikeys take time to accelerate when turning so you can quickly build up a big gap between Shuggy and the Spikey. When you reach the gap, jump up to level 3.
Now this bit is the same as the last level but in the other direction. So wait for Spikey 2 to pass under you to the right, then fall back down the gap before Spikey 3 gets you. As soon as Spikey 3 passes over you to the left, jump back up the gap and run right. When you reach the gap to level 4, jump up it.
Level 4 hardly has any room to the right of the gap to level 3, so we can't use the same trick again. But this time the gap to the next level (level 5) is not as far along. So, once Spikey 3 has passed back under you to the left, fall down the gap again. Then wait for Spikey 4 to pass above you to the right then back to the left. Jump up the gap and follow Spikey 4 along to the left. Jump up the gap to level 5 when you reach it, before Spikey 4 turns around.
Now you need to wait for Spikey 4 to pass back under you to the right and fall back down the gap before Spikey 5 gets you. This bit has the trickiest timing in the whole level. The space of time between Spikey 4 passing to the right and Spikey 5 running into you is very short so you need to be ready. Also, whenever you jump up to level 5 and are planning on falling back down, jump up to the left of the gap as it will give you marginally more time before Spikey 5 hits you.
Now, back on level 4, run to the left, collect the gem there, then back up the gap to level 5. Unfortunately you now need to do the same tricky move as before. Wait for Spikey 4 to pass below you to the right and fall down the gap. This time though, as soon as you fall down the gap and Spikey 5 passes over you to the left (which is very quick) jump up and to the right. Then run for the gap to level 6 and jump up it.
You could try and collect the gem to the right before jumping up the gap to level 6 as I think there is enough time, but I advise against it. Instead use the spare time to make sure you line up with the gap properly. It's easy enough to come back down for the gem.
So, wait for Spikey 5 to pass under you to the left. Then fall down the gap to level 5, run to the right, grab the gem, then back up the gap.
Now, again wait for Spikey 5 to pass under you to the left and fall down the gap. This time as soon as Spikey 6 passes to the left, jump up and to the right, collect the gem and back down the gap.
Then, when Spikey 6 passes over you to the right, jump up and all the way to the left, collecting the few remaining gems. You don't need an escape plan for this bit, since the level finishes as soon as you have collected all the gems.