Played this for the better part of an hour just now. Managed to get a lot of gold/platinum relics. Four more to go.
It's painfully obvious that the levels of the first game haven't been created with time trials in mind. That's probably be the reason why some of times are very lenient. The biggest problem is completing the levels without dying.
Never played the second Crash Bandicoot, but there haven't been time trials, either, until this remake, have there?
Really looking forward to the relic hunt in Warped. The levels clearly have been created with a certain speed run mentality (which is emphasized by the final upgrade for Crash).