Learn Finnish: Epäonnistumisista huolimatta emme pelkää kritiikkiä. - Despite failures, we are not afraid of criticism.

The postposition huolimatta (despite) dictates the case here. It requires the noun it belongs to to be in the elative case. Since the sentence talks about failures in the plural, we use the plural elative form of the noun epäonnistuminen.

Can huolimatta go before the noun instead of after it?

Yes, huolimatta can function as both a postposition and a preposition. You could perfectly well say huolimatta epäonnistumisista without changing the meaning, though putting it after the noun is generally more common in Finnish.

Break down the word epäonnistumisista for me. How do we get from the root to this form?

It starts with the verb onnistua (to succeed). Adding the negative prefix epä- gives epäonnistua (to fail). Turning that into a noun with -minen creates epäonnistuminen (a failure). The stem for this noun type ends in -s, making it epäonnistumis-, to which we add the plural elative ending -ista.

As a quick refresher, why is kritiikkiä in the partitive case?

The main verb in this clause is pelätä (to fear). In Finnish, verbs that express an emotion, feeling, or attitude toward something almost always require their object to be in the partitive case.