I am going for all platinum relics here (as well as on The Huge Adventure, but I don't think I'll have too many problems there -- I already have all platinum relics for the first warp room), and there are just four levels getting in my way: Globe Trottin' Barrel Roll Rocks Can Roll Spaced Out For the first three, I can't even get the sapphire relics. Not so much the time limit, but I can't even make it to the end of the level. For the last one, I've managed 2:49:00 for the gold relic, but I had a hard enough time getting through the enemies for that time. Platinum relic requirements are 0:31:50, 1:07:00, 0:55:70, and 2:30:90, respectively.
Any help? In the meantime, I've gotten platinum relics where I could in Crash Bandicoot: The Huge Adventure, but I'm having problems there as well. However, I don't want to create a help thread on that until I get the platinum relics for the levels I listed in the OP above for this game.