Sypha's a witch.
She uses elemental anima magic (Fire, Ice, Lightning), by harnessing the energy of spirits to control the elements.
The fact that she works for the Church is precisely to prove to the Church that witches aren't evil and have been oppressed by the church wrongfully. Supposedly her witch sisters were hunted down by people whose hearts were clouded by evil (an effort in which Carmilla took part), and escaped and took refuge in a monestary, where she lived for some time and became a Monk, while developing her powers until mastering them.
When the monsters of legend started attacking villages after Dracula summoned them to do his bidding once he became a powerful sorcerer, the Eastern Orthodox Church decided to fight the hordes of monsters back so it sent an army to fight them. In addition, the Church sent a special team of people with powers to deal with the threat in secret. Sypha was part of this team. The Church knew that the Wallachian populace was afraid of witches and pretty much any people with supernatural abilities, so they sent Sypha in disguise. Unfortunately, the team failed and Sypha was captured and petrified by Cyclops*.
When the Eastern Orthodox Church sent Trevor Belmont, that was their absolute last resort; the army had failed, the special team had failed, and there was no other known person that could both be trusted and be powerful enough to take on the Dracula threat.
*Personal note: I actually think that the Cyclops is Medusa's Pet, and Medusa actually petrified Sypha while the Haunted Ship was docked near the Statue Garden where the Cyclops presides. Personally, I think the 'special team' tried to hop on that ship and was spotted. But that's fanfic material.
