I don't normally make comments about other corrections, but the one that you have received so far contains enough mistakes and omissions that I recommend disregarding it.

Italy was eliminated

1/ In English you would never say "happened something"; it would always be "something happened".

2/ You could say "a drama" happened since "drama" can be a single incident. However you would rarely hear a native speaker use it as a noun for something like this. They would normally use it as an adjective; "something dramatic".

3/ Italy is a noun, Italian is an adjective. You can't say "Italy team", but you can't say "Italian team" by itself either. It would always be THE Italian team if referring to the one national team. (It would be AN italian team if you're referring to a club like Juventus, AS Roma, etc.) Either way, the word "team" needs an article.

4/ You don't "qualified to" something, and you don't "qualify to" either. The act of qualifying qualifies you for something. (You would only ever use "qualified to" in the "essere" sense; "He is qualified to install electrical wiring". It's a state of being, not an action.)

5/ The name of the competition is actually "World Cup".

It is very a bad thing for all the entire Italian soccer movement.

1/ You can't use "all" with something singular; in this case "movement". For it to affect "all" things, there must be more than one "thing". You could say "It is a very bad thing for all Italian soccer clubs and players", since clubs and players are plural.

I'm going to continue this in another correction because of Italki's character limits.

Part 3: Please read parts 1 and 2 first

The succeeding World's Cup was played in the USA and Italy arrived in the final versus Brazil (with Ronaldo), but Italy again lost after the penalty series shoot-out.

1/ Contrary to what you may have been told earlier, it is NOT correct to say that a team "arrived to" the final. You arrive in a place, or you arrive at a place, but you do not ever arrive to a place in English. That said, I would not use "arrived" in this sentence. Not because of the grammar, but because it suggests that the team just "turned up" rather than working for it. I would say that Italy "made their way to the final" (yes, "to" is OK with "way"), or perhaps that they "won through to the final".

2/ ""Final" also needs an article; you need to say either "the final" or "a final", not just "final" by itself.

3/ I'm going to leave "versus" in place here; as I said, it's not really wrong as such.

I remember very well all of the things that happened in this World's Cup.

"I remember ... all things" would be used if you remembered every single thing at every single place and time. "I remember all of the things..." is more limited and, in this case, accurate.

2/ You can't say "I remember all of the things happened"; it would be "all of the things that happened" or "all of the things which happened".

3/ "This" is ambiguous. I don't know whether you are talking about the 1990 World Cup in Italy, or the 1994 one in the USA, or the 2018 one in Russia since you've spoken of all of them. In particular you mentioned both the 1990 and 1994 ones in the previous sentence. I recommend replacing "this World Cup" with  whichever one(s) you are thinking of.

The bulk of your document is well written; leaving aside any grammatical issues you got your meaning across well.

Part 2: Please read part 1 first.

1/ You could say "I don't remember", but in this case I would probably use "can't". There is a subtle difference.

"I don't remember a similar thing having happened" = "It may have happened, but I don't recall it."

"I can't remember a similar thing having happened" = "I don't think that such a thing happened before now. I may be wrong, but I doubt it."

2/ Again, you can't say "happened something". I would probably have said "I can't recall a similar thing having happened", but your version is OK.

I remember when I was younger and in particular when it was the 90's and there was the World's Cup in Italy.

1/ Just as with "team" you can't say "90's" by itself; it is "the 90's".

There was a spectacular atmosphere and all people everyone watched all match of the Italy of the matches in which Italy played.

1/ "All people" isn't really wrong, but you wouldn't usually hear a native speaker say it that way. "Everyone" or "everybody" would be the normal way of saying it.

2/ Unlike in Italian, you don't generally put "the" in front of a country's name unless the name represents a plural; for example, "the United States", or "the Bahamas". However you can't use "match of Italy" either. Nor would I recommend saying "all Italian matches", since if the tournament is held in Italy they will ALL be "Italian matches" in one sense. I would therefore say it as I have shown above, though you could also say something like "all of the matches which featured Italy" or "all of the matches of the Italian team".

Unfortunately, Italy lost in the semi-final versus against Argentina (with Maradona) after the penalty series shoot out.

1/ "Semi-final" also needs an article; "the" if you're referring to one specific semi-final (as you are here) or "a" if it is some non-specific one.

2/ "Versus" is not completely wrong here, but would normally be used to describe the actual match "Tickets for the Italy Versus Argentina match go on sale next week" rather than who the opponent is. Using "versus" would be understood but I'd prefer to use "against" in this sense.

3/ A "series" is usually a group of discreet and distinct things. For example, Series A is a series of matches. It would not normally be used just for one part of a game. In English the term "penalty shoot-out" is usually used for this.

I'm going to continue this in a third part because of the character limits.

Italy was eliminated

Bravo. 

Mi dispiace per l'Italia.

VI auguro lo meglio, e in bocca al lupo per la prossima volta.

Buona serata.