He was well-known, but dueling Grindelwald was likely his crowning glory.
Dumbledore wasn't an unknown wizard before his defeat of Grindelwald, he was fairly successful as a skilled wizard and innovator. However, his defeat of Grindelwald seems to have escalated him to new heights of renown. The information we have on Dumbledore's early years is mostly from two different biased sources, Elphias Doge and Rita Skeeter. Elphias Doge's Albus Dumbledore Remembered is a hagiography without a single even slightly negative word to say about him, and Rita Skeeter's The Life and Lies of Albus Dumbledore is written to maximize scandal and shock, so is more derogatory than needed.
Before defeating Grindelwald, he was likely well-known enough but not famous.
Right before he duels Grindelwald, he's known to be a skilled wizard, he's a teacher at Hogwarts, and he's been offered the position of Minister of Magic multiple times. He's probably well-known and respected, but might not be "famous" since even very academically successful people aren't always famous, certainly not at the level that defeating a notorious Dark wizard who was successfully conquering the world until then would bring.
Timeline of Dumbledore's life and levels of fame:
Born 1881 - Presumably not particularly famous at that point.
When Dumbledore was born, at least to our knowledge, his family wasn't particularly famous or notable, so he wouldn't have been famous or noticed much at birth.
Life before Hogwarts (1881 - 1892) - Mild infamy after his father's attack on the Muggles.
Before attending Hogwarts: His sister Ariana is attacked by Muggles who saw her do magic, causing her to become unstable. His father then attacks the boys but doesn't admit to the real reason that he attacked the Muggles, to protect Ariana. His mother then chooses to move to Godric's Hollow, probably to escape the negative effects of the bad reputation her family had because of her husband's crimes and sentencing.
From Rita Skeeter's book The Life and Lies of Albus Dumbledore:
“Proud and haughty, Kendra Dumbledore could not bear to remain in Mould-on-the-Wold after her husband Percival’s well-publicised arrest and imprisonment in Azkaban. She therefore decided to uproot the family and relocate to Godric’s Hollow, the village that was later to gain fame as the scene of Harry Potter’s strange escape from You-Know-Who.
Like Mould-on-the-Wold, Godric’s Hollow was home to a number of wizarding families, but as Kendra knew none of them, she would be spared the curiosity about her husband’s crime she had faced in her former village.” - Harry Potter and the Deathly Hallows, Chapter 11 (The Bribe)
While many of the presumptions like Dumbledore's mother being motivated by her pride and haughtiness are probably false, it seems likely that she did choose to move because of the events surrounding Ariana.
Starts Hogwarts 1892 - His only "fame" is that his classmates think he hates Muggles.
From Elphias Doge's biography:
“For his part, Albus had arrived at Hogwarts under the burden of unwanted notoriety. Scarcely a year previously, his father, Percival, had been convicted of a savage and well-publicised attack upon three young Muggles.” - Harry Potter and the Deathly Hallows, Chapter 2 (In Memoriam)
It seems logical to presume this is true. Dumbledore suffering under the reputation of his father is a negative sort of thing, and it's mentioned by Doge, who generally says only the most positive things about Dumbledore. While it isn't wholly negative, as it can be seen positively as Dumbledore overcoming unfortunate circumstances, I doubt he would have made it up if it wasn't true.
First year (1892 - 1893) - He's able to get past his father's image and is seen as very bright.
“In a matter of months, however, Albus’s own fame had begun to eclipse that of his father. By the end of his first year, he would never again be known as the son of a Muggle-hater, but as nothing more or less than the most brilliant student ever seen at the school.” - Harry Potter and the Deathly Hallows, Chapter 2 (In Memoriam)
Again from Doge, this quote states that Dumbledore is able to entirely overcome his father's reputation, and is instead thought of as the most brilliant student to ever attend Hogwarts. It seems highly likely that Doge is probably exaggerating at least somewhat, but the basic idea is probably true.
Hogwarts years (1892 - 1899) - He's a very successful and applauded student.
More from Elphias Doge:
“He not only won every prize of note that the school offered, he was soon in regular correspondence with the most notable magical names of the day, including Nicolas Flamel, the celebrated alchemist, Bathilda Bagshot, the noted historian, and Adalbert Waffling, the magical theoretician. Several of his papers found their way into learned publications such as Transfiguration Today, Challenges in Charming and The Practical Potioneer.” - Harry Potter and the Deathly Hallows, Chapter 2 (In Memoriam)
All of this is likely true, as Doge didn't seem to be intentionally lying, and everything said there would be provable. What awards Dumbledore won and who he corresponded with would be knowledge that Doge would have, and that he couldn't be mistaken about due to his high opinion of Dumbledore.
From The Life and Lies of Albus Dumbledore:
“Now approaching his eighteenth birthday, Dumbledore left Hogwarts in a blaze of glory – Head Boy, Prefect, Winner of the Barnabus Finkley Prize for Exceptional Spell-Casting, British Youth Representative to the Wizengamot, Gold Medal-Winner for Ground-Breaking Contribution to the International Alchemical Conference in Cairo. Dumbledore intended, next, to take a Grand Tour with Elphias ‘Dogbreath’ Doge, the dim-witted but devoted sidekick he had picked up at school.” - Harry Potter and the Deathly Hallows, Chapter 18 (The Life and Lies of Albus Dumbledore)
After graduating (1889) - his future seemed bright but his mother's death caused him to stay home.
Shortly after he graduated, Dumbledore's mother died, meaning he needed to cancel his plans to travel around the world to return home to take care of Ariana so his brother Aberforth could finish his schooling. He probably isn't particularly famous at this point, because although he had been quite successful as a Hogwarts student, at this point he drops out of view of the rest of the wizarding world completely. He meets Grindelwald during this time, and his return to pursuing a career is brought about by his sister's death, which itself is the cause of his falling out with Grindelwald.
As Dumbledore explains it to Harry:
“So that, when my mother died, and I was left the responsibility of a damaged sister and a wayward brother, I returned to my village in anger and bitterness. Trapped and wasted, I thought! And then, of course, he came …’
Dumbledore looked directly into Harry’s eyes again.
‘Grindelwald.” - Harry Potter and the Deathly Hallows, Chapter 35 (King's Cross)
After Ariana's death and his split with Grindelwald (1889 - 1945) - his good reputation grows.
Once his sister was dead and he no longer wanted to associate with Grindelwald, there was nothing further holding him back, so presumably he began pursuing a career in the wizarding world. At some point, which is explicitly mentioned as being before his duel with Grindelwald, he is offered the post for Minister of Magic multiple times.
“Years passed. There were rumours about him. They said he had procured a wand of immense power. I, meanwhile, was offered the post of Minister for Magic, not once, but several times.” - Harry Potter and the Deathly Hallows, Chapter 35 (King's Cross)
That's also when he becomes the Transfiguration teacher at Hogwarts.
“I was safer at Hogwarts. I think I was a good teacher –’
‘You were the best –’
‘You are very kind, Harry. But while I busied myself with the training of young wizards, Grindelwald was raising an army. They say he feared me, and perhaps he did, but less, I think, than I feared him.” - Harry Potter and the Deathly Hallows, Chapter 35 (King's Cross)
In Fantastic Beasts and Where to Find Them, we discover that Dumbledore is able to convince the staff of Hogwarts not to expel Newt, despite being the Headmaster yet, implying he's fairly respected.
The time of some of his achievements, like his discoveries about dragon blood, is unclear.
From Elphias Doge's Albus Dumbledore Remembered:
“Other quills will describe the triumphs of the following years. Dumbledore’s innumerable contributions to the store of wizarding knowledge, including his discovery of the twelve uses of dragon’s blood, will benefit generations to come, as will the wisdom he displayed in the many judgements he made while Chief Warlock of the Wizengamot. They say, still, that no wizarding duel ever matched that between Dumbledore and Grindelwald in 1945.” - Harry Potter and the Deathly Hallows, Chapter 2 (In Memoriam)
These are all objective facts Doge says other people will mention as well, so we can safely presume they're all true. From his saying "the triumphs of the following years" we can reason that these achievements all happened after Dumbledore graduated. However, the order in which he did them is less clear. It doesn't seem reasonable to presume that the duel happened last because it's the last thing mentioned. It could be mentioned last because it's his most famous accomplishment, and Doge is "saving the best for last" or listing them in increasing order of importance.