Learn Portuguese (Portugal): Faça o que fizer, ele não vai alcançar o triunfo. - Whatever he does, he will not reach the triumph.

This is the core formula for this type of concessive expression. The first verb (faça) is in the present subjunctive, and the repeated second verb (fizer) is in the future subjunctive. Together with the relative words o que, this creates the meaning of 'whatever [subject] does'.

Can I use this same 'present subjunctive + o que + future subjunctive' pattern with other verbs?

Yes, it is a highly productive pattern! You can apply it to almost any action. Common examples include diga o que disser (whatever he says), custe o que custar (whatever it costs), and aconteça o que acontecer (whatever happens).

How do we know 'Faça o que fizer' means 'Whatever HE does' if the word 'ele' isn't there?

The subject is implied by the main clause that follows (ele não vai...). Because the verbs faça and fizer are conjugated in the third-person singular, they perfectly match the ele of the main sentence. You could say Faça ele o que fizer for extra emphasis, but the pronoun is usually dropped here to sound more natural.

Why does the second half use 'vai alcançar' instead of the simple future tense 'alcançará'?