This a fixed expression in English - "tense times" would probably be translated as "tempos tensos" or "tempos de tensão" ("time" being a longer timeframe than a "moment").
Can't we say tension moments?
No, it's a fixed expression in English.
Is it in Portuguese? As a native English speaker it sounds a lot more like a Romance language calque than something with a unique life of its own in English. "Tense moments" I'd much more readily classify as approaching fixed-expression territory.
'Tense Moments' is correct as well.
Why not "tension moments"?
A bit late but I don't think that's correct english. Tense moments is accepted.
Tension and moments are both nouns. You need an adjective and a noun.