The fee to enter endgame raids is 6 Raid Portal Stones. You get the recipe by doing Challenge Mode and opening reward cubes (random drop from cube along level 315/350 mats). To craft the recipe, you also need 30 Nucle Powder and 15 Sierra Powder, so it’s a good idea to dismantle any random blue/purple/orange you get with bad stats and do Uphill missions.
Note that Raids are grindfests, as the reward for completing them is also a cube that has random stuff inside. You have 10% chance of getting a random recipe (so if you want an Asio staff, the chance you get the recipe is pretty slim – you’ll probably have to trade the random recipe you get for one), 5% chance of getting some badly needed Practonium (each recipe requires 3 Practo, which per se isn’t a problem since you get 3 guaranteed by doing 2 mere quests), and 85% chance of getting a “fragment” (the trash item – you will need 50 of them to get another random recipe, which means gathering 300 Raid Portal Stones and do the raid 50 times… ouch). You also have a slim chance of getting a recipe for an Ancient Gold Socket (the thing you put in your equippables if you don’t have the potential for another socket), but you shouldn’t bother with that.
At level 390, you can still do dun330 runs for the 100k silver + the class xp (usually you’re not at class 45 when you reach level 390 – my last char reached class 41 at that point) + the talt (that’s for your guild if you’re in one). But your best bet is Challenge Mode: you will need the Raid stones, the silver it gives, the trash drops for Powder or enhancing gems. Once you get your recipe for level 380 item (Asio staff or other), you will have to get the mats to craft it. Each recipe requires only 1 type from monster drops, so go to the map where it drops and do CM there. Solo CM stages 1-3 is enough to get 7-10 of those mats per run, or you can shout for a stage 6-7 CM party. Asio also requires sapphires, you will have to buy them or grind them from HG.