Getting all platinum relics in Crash 3 requires a very challenging learning curve. You basically have to be flawless in your time trials in order to get a Platinum. I think I only got 5 when attempting to get some. It is just too frustrating for me to get them because I know I will never be flawless on my playthroughs. But some people have done it before.
The hardest level are definitely the Coco skiing and Arabian themed levels.
I got a platinum in Midnight Run. You essentially have to use boost all the time with Pura, make every jump, and collect every box as possible to get a platinum. It requires a lot of perfect, but it not too bad as those levels are insanely fun.
Over the past couple of weeks or so I've been playing through the game for the first time (better late than never!) on my PS2 in some of the measly free time that I have these days (the PAL version by the way, as I live in the UK; allegedly it's slightly harder!), and I'm well on my way to having a platinum relic in every level. I'm quite experienced with games of this genre and used to do some IL speedrunning, so I suppose I'd find it easier than the average gamer. (I don't mean to sound vein or anything here, I'm just stating my case! =P)
The difficulty in obtaining a platinum relic varies from level to level, sometimes quite drastically -- some platinums didn't take me long at all to get while casually playing, whereas some others took quite a lot of work and I had to push myself! Either way, they're all pretty difficult to get to some degree, and whilst the process so far's been fun from beginning to end for me, I've often gotten marginally frustrated and annoyed! Nevertheless, it shouldn't take me long to pick up the platinum relics that still await me. ^_^
The Orient Express and Midnight Run time trials are actually pretty tough in the PAL version, but it didn't take me that long to get a platinum in either. The Coco Jet Ski levels are definitely amongst the hardest to get platinums in; they took me some time. I personally found the Arabian and Medieval levels amongst the easiest however.
Level 32- If you're having trouble getting it on Coco's ski levels, I know how to get it for this one. Ignore the gem, just pay attention to the relic. Behind you will be a line of Nitro crates "guarding" the warp for ending the level. Just go to the side and on one of the ramps, there would be a Nitro detonator thingy. Activate it and go back to the beginning of the level and there you have it.
With the recently discovered techs like Zigzag, Restart Glitch and Neutral Slide-Jump, getting all the Platinum Relics has become extremely easy. You don't need to be flawless in your run! In fact, all the Platinum Relics in the platforming (running) levels can be obtained without the Speed Shoes.
Yes, it's tech used by Time Trial players to get better times. It is performed by pressing "Left" and "Right" buttons really fast while running ("Up" and "Down" buttons if you are playing in a side-scrolling part of levels like Future Frenzy and Gone Tomorrow). By doing that, Crash gets unlimited speed boosts, depending on how well you execute the tech. However, this feature has its downside, and that is the fact if you use it constantly and for a very long time, your thumb will be in pain. Personally, I detest this tech, but there were many fakers setting unreal World Records in Crash 3, so it was mandatory for me to utilise it and beat their times, so a fair player could have the best times in the game.