Frontier coins can be earned from opening some of the rarer soul forms (Lilith, for example), from Gauntlet and Arena rewards / events, and occasionally from other events.
There are a few types of characters you can purchase with these, and a few characters that you can't get any other way. We'd encourage you to focus on those that don't show up anywhere else and slowly collect those that can be found elsewhere.
Angel and Gambler
Two of the game's most powerful eddies. Buy a 50/50 soul with fragments, costing in total 2500 FC, or a guaranteed one for the one you want for 4500.
Killer Prime and The Ferryman
Two of the game's most powerful allies. The price is steep, but they are both worth it. Get KP first if you have to choose.
Only available from a Beast Soul, The Beast is one of those characters that many covet. He's got some great abilities, but his high cost makes him a "down the road" goal and not something for beginning players.
Trooper Eddie, Lady Azov, Bastion and the Warlord can be obtained randomly from Trooper souls, or you can purchase them for Frontier coins. We generally recommend buying trooper soul fragments weekly with trooper badges and only buying one of these if it's the last one you need for your collection from this group and you've been getting duplicates of the others quite regularly.
Eternity Eddie, The Clairvoyant, Wrath and Beelzebub can be obtained from Eternal souls from the Arena store. While it'd be great to obtain them that way, we also realize that those arena rewards are tough to come by and should probably focus on buying relics first and foremost. The fragments for Eternal souls also come as arena rewards, so keep in mind that some of these will eventually fall in your lap if you keep playing.
With the addition of Lilition in 5 flavors (Warrior, Magus, Sentinel, Gunner and Assassin) to the game, we were introduced to some hard hitting female characters. They each have unique abilities, so having this entire collection is really desireable. From reviving and healing to heavy hitting, blocking and golden buff transformations, this is a very powerful set of characters. They are all available from Lilith souls, which you can earn fragments for during fragment events in the LoL dungeons, but it seems most players end up grabbing 1 or 2 from the Frontier store.
Not currently available anywhere else since their launch event, Goddess Aset, Goddess Sekhmet, Osiris, Set and Horus are a unique class. Again, each has a unique ability to make the entire set a must have at some point. For many players, Osiris or Horus have been game changing additions to their rosters. These are some that you should certainly be using Frontier coins for since they're not available anywhere else.
One of the most unusual Eddie characters in the game, Alexander has no fury attack and instead boasts a passive ability that is well worth taking note of. While most of the Eddies struggle to farm Number of the Beast, Alexander is immune to the effects that The Beast uses to stun and lower your defenses, so he is actually one of the most reliable to use on that particular level. He also is very useful in Arena, Gauntlet, and any other stage where you want to make sure not to be stunned or frozen. While his cost is higher than most, the value from attaining him makes it well worth the time investment.
These are the only way to open the frontier dungeons and get their exclusive characters. Priced between 175 and 250 a piece, choose wisely. Hint : the trooper ones can be bought with trooper badges from the trooper store.
There are some specialty talismans available in this aisle of the store. They are generally considered stronger than the ones you can easily farm, but also provide unique abilities that extend your character's abilities. Check them out and decide for yourself if you could use some of them. I should also mention that they are sometimes required for completing events.