Leave this until you get the Speed Boots at the end of the game after beating the final boss.
27 Relics is all of them and Gold is the second highest rank available of three (It goes Sapphire, Gold then Platinum).
The key is to obviously go fast in each level and make it to the end as quickly as possible, all the while smashing the time crates to freeze the clock for as many seconds as it displays on the box. The Speed Boots are vital to getting most of them so hold R2 while running to use the Speed Boots and get a massive boost to your standard running speed.
I'm not going to do a tutorial on each and every level as there are obviously a lot of them but a good tip while doing this is to slide jump whenever you get the chance. I found this preserves momentum and speed when jumping over obstacles and is good even on flat tracks to go faster.
Turtle Woods and The Pits are surprisingly some of the tougher times to beat and to even get Gold you really need to get at least somewhat consistent with clearing the pits from the other side. You have to essentially slide, spin and jump all in one motion (that's a slide, spin and then jump while running) at the initial edge to get the distance necessary and it can be quite tough to pull off. Keep practicing this key technique to the point where you can at least clear one of them, as that was what I found was needed in both of them (actually I think it might have been 2 in Turtle Woods).
On the Polar levels the key is to dash jump whenever you can and for the jetpack levels just keep moving and hit all of the time crates.
Probably the hardest Gold Relic in the game in terms of strictness is Hangin' Out. It demands you take a lot of risks going past some of the robots. One key time save I will point out is near the start when you initially drop down to the first monkey bars. From here, slide jump from the left side to the further part of the bars.
Piston It Away and Spaced Out are also quite difficult (and more aggravating) due to the hitboxes of the octopus robots, the quality Nitro programming (nice job Vicarious Visions) and the cycles of the pistons to contend with. One tip I can give at the start of Piston It Away at least is to wait until the first piston drops then grab the clock and it should raise by the time you get there. I've also seen people kill the first enemy before grabbing the time crate as it isn't far enough away that the game despawns the clock. That should hold you in good stead for the rest of the level but it is really difficult.
Anyway good luck! It isn't easy but you'll likely feel very satisfied after getting that last Gold :).