The simplest way is probably to kill a whole lot of enemies. After you reach floor 120 of the mines, enemies gain more HP but they also gain a 1/200 chance of dropping a prismatic shard. The fastest way is probably to go to floors 45, 55, and 65 of the mines via the elevator, kill any enemies relatively near the entrance (don't bother walking too far), go back to floor 0 to reset the mines and repeat. I suggest those floors in particular because they spawn dust sprites, which a) tend to spawn in groups of several enemies so you can kill more enemies at once, and b) drop coal which you will probably want anyways.
(For anyone else seeing this question who might be on PC, you can use the
Stardew Predictor website to see what geodes will give you. The results of a geode depend on the total number of geodes of any kind opened so far. So for example, if you have only one omni geode but you see that 4 geodes from now an omni will give you a prismatic shard, you can open three geodes of any other kind and then open the omni as the fourth geode to get the shard.
Unfortunately I don't believe you can access save files on XBox, but if you happen to know the seed number of your file, you can still use the Stardew Predictor by manually entering the seed number in the URL - e.g. go to
https://mouseypounds.github.io/stardew-predictor/?id=611235816, but with the number in the URL replaced by your seed number.)