As to lines 2 and 3, there are ut clauses that follow comparatives (see, for example, Allen & Greenough, New Latin grammar, §535, c); however, (1) they require a quam; and (2) they mean, e.g., 'too foolish to...' rather than 'foolish enough to....' Therefore, although this construction works for line 3 of your statement, it doesn't work well for line 2.
Instead, for 'foolish enough to try to change the world,' I suggest satis stulti (genitive, to agree with militis, as Joonas noted in his answer) + ut + subjunctive.
This use of satis + ut + subjunctive can be found in, e.g., Livy, Ab urbe condita 7.9.11 (granted that satis in this example is a predicate adjective, not an adverb):
Fabio satis visum ut ovans urbem iniret.
To Fabius is seemed sufficient that he enter the city in an ovatio.
So, combining the two constructions, you could say:
satis stulti ut mundum mutare conatus sit,
firmioris quam ut mundo mutari potuerit
foolish enough that he tried to change the world,
stronger than that he was able to be changed by the world.
(Note that I've preferred to use a perfect subjunctive in both lines.)
I'm not sure about mundus, though it may be correct; it depends what you mean by 'the world' in this context. 'Bradley's Arnold' Latin prose composition, §16, b has a nice summary of the issue:
Again, we might meet with the word 'world' in an English sentence; but we cannot translate it into Latin till we know whether it means 'the whole universe,' or 'this globe,' or 'the nations of the world,' or 'people generally,' or 'mankind,' or 'life on earth.'
Num cāsū factus est mundus? Was the world (sun, moon, stars, and earth) made by chance?
Lūna circum tellūrem movētur. The moon moves round the world (this planet).
Orbī terrārum (or omnibus gentibus) imperābant Rōmānī. The Romans were rulers of the world.
Omnēs (hominēs) īnsānīre eum crēdunt. The whole world thinks him out of his mind.
Nēmō usquam. No one in the world.
Multum hominibus nocuit. He did the world much harm.
In hāc vītā numquam eum sum vīsūrus. I shall never see him in this world.
Joonas's innominatus may very well be the best solution for 'nameless'; but again, I think it depends what you mean by 'nameless' in this context. If you mean that the soldier's name just isn't known, something like militis nomine non noti ('a soldier not known by name') might be more accurate.
Finally, I believe perpetua memoria (ablative) should be perpetuam memoriam (accusative).