Each Main Episode has at least 3 Secret Coins to unlock: two of which will be in blue chests that will appear on the map when certain conditions are met, and the 3rd if you obtain a overall S-Rank for the episode. I'll explain how to get all 3 coins using Prologue Episode 2 as an example:
A) Obtain an overall S-Rank
You need to get an S-Rank in the three categories: amount of time spent in the stage, amount of damage you take from enemies, and the number of enemies defeated. In short, you need to finish the stage fast, take little or no damage, and beat up a LOT of enemies. The times vary per stage, and so does the amount of damage you can take (though I could be wrong), but the number of defeated enemies should be over 1200 (An A-Rank is over 1000 enemies defeated). My stats for Prologue are thus:
Clear Time: 11 minutes, eight seconds
Damage Received: 9 (I think anything less than 100 would count as an S-Rank)
Minor note - do NOT play on Easy, as you will only get as high as A-Rank on Easy. You need to play on Normal to be able to achieve S-Ranks.
Your secret coin for this will unlock at the end of the stage after you're ranking is confirmed.
B) Reach 1000 K.O.s
In short, you need to defeat 1000 common enemies before the blue treasure chest will appear. Once your count is confirmed, an indicator of a glowing green circle will appear on the mini-map to show where the chest holding the secret coin is located.
C) Without Smoker fleeing, defeat all army generals
This is what I call an "objective requirement," as these will happen frequently throughout the Main Episodes and each one will be different per Episode. In Prologue Episode 2, you will need to defeat all the army generals and make sure Smoker doesn't get defeated and flee in the process. These specific generals will only appear when you are trying to make your escape back to the Thousand Sunny, and they will be indicated by yellow dots on your mini-map. The best strategy is to confront each general when your style gauge is full and then use it on them. When your style action runs out and they're not defeated yet, keep your distance and let your gauge refill. Lather, rinse, repeat.
Note: there will be 7 army generals total, and most of them come in pairs, so focus on one general at a time and keep a lookout for their "partner" in case he tried to attack you while you're fighting. If you're having trouble with these generals, level up your character by playing more of the main storyline and/or crew episodes and then come back to try again.
I hope this helps.