Completed the game in under 8 minutes. No shortcuts.
To complete the game in under 8 minutes starting from the Mines, you will need to learn a balance between rushing and patience. You'll have to be smart about this speed run, making sure not to go out of your way for treasure, a damsel, or certain items. If you can manage to get a jetpack, cape, or compass, you will have a much easier time going for this. If you don't get a compass you might want to just start over.
You should be able to clear the mines fairly quickly. You'll want to have less than 2 minutes used up by the end of the Mines. The Jungle will most likely take you the longest time. Your limit for the end of the Jungle should be 4. The Ice Caves should take the least time if you have a cape or jetpack. Try to finish the Ice Caves with only 5 minutes used up. The Temples can take a while as they are possibly the most difficult stages. Reaching Olmec with 7 minutes is a good goal to give you enough time to defeat Olmec. See the video guide for my details.
I have been practicing for the low score achievement and I accidently picked-up a gold piece but realized I have a compass and have good time in. Finished in 6:55 and almost died at the final boss since I was unconscious w/ a orange frog ready to explode. Luckily I got back up quick enough to get away :)
This achievement was really a pain in the ass. After like 6 hours I finnaly got this 10G and finished with a time of 6.52 mins. I think you really need to be patient and lucky. I think I restarted the game like 250 times. Now I had a fast time, enough lives and had 23 bombs at the boss. With all these bombs I made a big hole, trew out 2 ropes and lured the stone guy into the hole. I think you can do this without bombs by just running right and left while he crushed the floor away, but i failed at this pretty much :P.