Alright, it wouldn't let me edit my message so here's some general rules I followed. You'll want to make sure you go through the mines as quickly as possible while taking as little damage as possible. The ice caves are great for time, especially if you have a compass or cape/jetpack.
1. Risk vs. Reward - This is probably the most important thing to remember while you are trying to reach the exit. I never bother with chests, but damsels and crates are usually worth going a little out of the way for a random item or extra hit. Just make sure you won't take any damage or you might end up wasting precious seconds.
2. The Boot Trick - Pretty simple concept. Carry around an item and use it to set off any traps in the room ahead. Damsels make great pincushions if you know you can't avoid triggering the trap without getting damaged. You can also use the jungle frogs to trigger tiki traps.
3. Bombs - You'll want as many bombs as you can possibly find. Using them to create shortcuts is a great way to shorten your times, but make sure you save plenty for the temple. If you don't have any weapons, they might be the only way for you to get around an Anubis.
4. Olmec - Olmec is extremely easy, but unless you have a lot of bombs, it will take you about a minute to kill him. If you don't have 6:30 or less, there's a good chance you won't make it in time. Also, you'll want at least one rope or a jetpack. As soon as you can, run up to Olmec. He'll jump up once onto the same level as you. Run under his next jump so he does a ground pound. There should be just enough room on both sides for you to hug the wall without being crushed. Just run back and forth until he kills himself. Hopefully you won't get hit by any of his spawns and you can use your ropes as weapons if something is coming at you from above. --- GT: Joey Leen