Formal:
* Salungat na katotohanan (Contradictory truth)
* Kabalintunaan (Irony)
* Paradoha (Borrowed word, but not as common)
Informal:
* Kabaligtaran (Opposite)
* Magkasalungat (Contradictory)
* Nakakagulo sa isipan (Mind-boggling)
The best translation will depend on the specific situation and the nuance you want to convey.
For example:
* "The paradox of choice" could be translated as "Ang kabalintunaan ng pagpipili" or "Ang nakakagulo sa isipan na pagpipilian."
* "It's a paradox that he's both happy and sad." could be translated as "Paradoha na siya ay masaya at malungkot."
Remember, context is key when translating!