All Relics Needed on Xbox 360

There's 15 to be collected, not all of which will show up in the relics menu, they are as follows:
-Jetpack
-Speed Boots
-Jump Boots
-Water-Walking Boots
-Raygun
-Freezeray
-Night-Vision Goggles
-Helmet of Mobile Illumination
-TNT Detonator
-Lil' Digger
-Lil' Builder
-Spleef Gun
-Optical Camo
-Predator Blades
-Thermal Vision Helmet

The order these are obtained doesn't matter, however, it would be best to get the Jetpack and Speed-Boots first since they make movement much faster. But since you can't pick and choose which you get first, that's all dependent on luck.

The Helmet of Mobile Illumination is also good for the underground relics, which in my experience is most of them. The TNT Detonator can also help with this a lot as it makes digging for them MUCH faster.