The man stole ...
the MONA LISA.
Killing the two heads of URUGUAY branch Mr. Godin and Mr. Tabárez the gangster took away something very precious which doesn't belong to us.
Uruguay is written in capitals and the capital of Uruguay is Montevideo, and "killing the two heads" somehow seems to indicate to use the first two letters: MO.
The gangster is wanted alive and hence, shoot on sight option is simply not applicable.
The words not applicable are in italics and probably important. Not applicable can be abbreviated as N/A, or NA.
The criminal was last seen at Lithgow Small Arms Factory stealing two lethal weapons out of it.
I guess that stealing two lethal weapons means to take the first letters of "Lithgow Small Arms Factory", LI, but in cryptic parlance, I can't really see how. (I tried to remove the letters of weapons, for exaple Colt or Light Mortar, and then look at the remaining ones, but to no avail.)
Secret CCTV camera images shows that he was heading towards CHILE where he is going to take away the other two heads of the IBPS organization.
Same trick again: Take the first two letters of Chile's capital, Santiago de Chile: SA.
These clues don't follow the standards for cryptic clues even loosely. I've solved this with help of the first hints; (4, 4) and Arts lead to the Mona Lisa quickly. The rest was more or less solved backwards except N/A, which I had from the outset.
Addendum: I'll tyr to explain in detail why I think that the puzzle shoudn't be labelled as cryptic clues and I try to make some suggestions. Everything below is an analysis of the indtended solutions, so Spoliers Ahoy!
The problem with cryptic clues is that they cannot just be clues that are written in a more or less cryptic language; they follow strict rules. That's something many people here on PSE get wrong. In fact, I'm wary of any cryptic-clue tag unless the post is by Deusovi or Dan Russell.
These rules are outlined in Deusovi's post. They might differ slightly, foe example there seem to be differences in British and American usage, but on the whole, they are set. When you try to solve a cryptic crossword, you know what you're in for. When you try to solve a crossword without knowing the rules, you are usually stuck early and can't make heads or tails of the solution when you look it up. You can't solve (or set) cryptic clues without knowing the rules in the same way you can't play Chess without knowing and following the rules of Chess.
A very important concept of such clues is given in the first section of Deusovi's post: The clue has a definition, a subsidiary indicator and, and that's important, nothing else. That is, there should not be any filler words. The clue as whole should have a good surface reading: It should read like a meaningful sentence. And the setters are trying their best to mislead the solver. It is usually not clear which part is definition and which part wordplay and the words as used in the surface meaning often don't have the same meaning as used in the solution. A particularly popular device is to make verbs or adjectives appear as nouns in the surface and vice versa.
When you have solved the clue, you should see that all words have been used, either as part of the definition or as indicator for some device (anagram, juxtaposition, insertion, deletion, inclusion) or as fodder for such a device. Occasionally, setters can get away with filler words, but they should brece themselves for criticism on the crossword blogs.
Now your puzzle isn't a regular clue for a crossword. The definition is already given: We are looking for something that was stolen. That's okay. Crosswords sometimes do that as well. ("All down clues are missing definitions, but are thematically linked." That might appear in a crossword on a special occasion or anniversary, where the linked theme is easy to spot.)
And your clues must make sense as a story. And here's the problem: Only very little of your sentences is part of the wordplay. These parts are highlighted with all caps, italics and bold face, but most of it is filler. You've noticed it when people tried to find the solution in that filler text, namely the names of the two Uruguayan heads and the sentence about the arms factory.
And the clues, once you have isolated them, don't follow the rules either:
Using capital letters seems like a nice trick, but "Uruguay in capitals" isn't the same as "capital of Uruguay". (In cryptic clues, the captal of Uruguay can be Montevideo, but it could also be its capital letter, U.)
"Killing" would indicate taking away from the solution, so it's the opposite of what you intended.
It is clear that the third fragment is found in "Lithgow Small Arms Factory", but "two lethal weapons" doesn't mean the first letters. That's quite a strech, actually. If you mean letters you should either use some variant of letters of symbols or characters or just omit a noun and make the solver infer it: "the first two". (But you could remove the two weapons "gun" and "sling" from "gunslinger" to get "er".) In cryptic clues, "found in" usually indicates a hidden answer, for example "word" is found in "new order". It doesn't mean take some letters, and it doesn't indicate to take the first letters at all. And the phrase the wordplay operates on has four words of which the last three are filler.
So the problem with your puzzle is that you present something that isn't really cryptic clues as cryptic clues. You have mislabelled your puzzle and are going to disappoint solvers. (Old curmudgeons like me can still get some fun out of it by criticising it. Ha!)
There are basically two ways to fix this. The first is to make your puzzle a cryptic clue. That would mean to shorten the puzzle text, i.e. the quoted text, significantly. You can stick to the story of the stolen painting, but you could make the clue a classified ad that catches your eye:
Piece of art not available in outskirts of Montevideo, western half of Lima, primary quarter of Santiago (4, 4)
The solution would be
N/A in (M(ontevide)O + LI(ma) + SA(ntiago))
and while the surface reading isn't particularly smooth, it has a South American theme.
You could perhaps try to make the story more natural by making every other sentence a cryptic clue, but make sure to have some indication that only some sentences are cryptic.
The second solution is to make this a wordplay puzzle that isn't cryptic clues. In your puzzle, you use the first two letters of capital cities. You could extend this theme to all four two-letter fragments. Lima would fit with the South American theme. The second fragment could come from Nairobi or Nassau or from the Brazilian state of Rio Grande, whose capital is Natal:
IBPS agents have traced an individual trying to sell a valuable piece of art that was stolen last month. The thief was seen in various South American states where he tried to make capital of his goods by visiting the primary and secondary characters of the local illegal art dealing scene. So far, the thief has been in Uruguay, Rio Grande (Brazil), Peru and Chile.
Well, that's probably not a very good puzzle, but capitals and the first and second letters are loosely hinted at and there is a list to work from.