@kouch_lee:
But that's part of the question here: did he immediately go to Skypiea after being (violently) scolded by Dofla? Did he go a few months later? A year later? Did he go to Skypiea 2 days ago, killed everyone and burned everything to the ground? Right after the update we got on Skypiea and everyone was super happy, here comes the Hyena to kill you all? Improbable, I know.
Oh c'mon lets think logically, the skypieans (or at least what we've seen of them) are fine.
We can assume that there is a considerable time difference that is required for Bellamy to become "Dressrosa's protector" (one doesn't just pull that off in ONE day since it is stated that he attacked multiple settlements). That in itself would probably take a few months (if not, a half a year or entire year) unless Dofla is pulling strings in the background.
However, in order to do this, it is safe to assume he first won favor with Dofla through that skypeian pillar. Therefore, we can assume that Bellamy's timeline went like this:
1.Bellamy "not killed" by Doflamingo
2.Bellamy going to Skypeia
3.Bellamy going to Dressrossa
4.Bellamy gaining popularity in Dressrossa
5.Tournament
The time between 1-2 is still a tossup since it could have actually occured BEFORE the timeskip or during it. However, it is safe to assume that he took the more challenging route and lost his crew during the process or his crew was attacked by skypeans and eliminated. If he lost his men while getting to skypea, then he took the pillar solo, SOMEHOW returned back, and traveled to Dressrossa on his own (or just…tailed someone there shrug). It seems highly unlikely that he took the pillar solo since it would require him somehow getting back. So if his crew did perish ALONG the way to skypea, it is possible that he befriended them (weird thought huh?) and they assisted in getting him back to land. PS: if one wants to assume he was only in skypea for a short time, it would be easier to assume he befriended them and they simply handed him the pillar.
However, if he did fight the skypeans and lost his crew. The problem still lies with how in the world he actually returned with the pillar. Also, he probably would have been up in skypea longer while trying to navigate through the place, encountering enemies, etc...
This in itself probably took a few days.
Next is the trip to Dressrossa....a big question still lies with how in the world he got there in the first place. (complete toss up, but I still say the trip should take at least a week or so from Jaya...unless the Skypeans had a magical cannon that launched him to Dressrossa with the pillar).
Once in Dressrossa, he had to prove himself to Dofla (after getting his attention with the pillar) in order to gain such popularity (as he has now) and by attacking other establishments that are PROBABLY in the New World. Now consider, before doing this, Bellamy probably needs to be far more competent as a solo fighter than he was back in Jaya which meant that he needed to train (and based on his physique, it is clear he has been working out). The training in itself probably took...shrug a couple of good months or maybe even a year. The question then lies with whether he trained up in Skypeia, trained while going to Dressrossa, or trained at Dressrossa. Either way, it still probably took a while for him to get this big (unless some mysterious Garp-like figure pulled a Coby/Helmeppo).
After this, he began gaining popularity which required attacking MULTIPLE establishments (hence, he traveled from place to place which also requires time). Eventually he gained enough popularity and here he is at the tournament.
So in other words, he probably went to Skypeia PRETTY early after getting slashed in the chest by Dofla.