I would say
Dark Angels - Theres no real definitive source on any speciality during the Great Crusade, but the Lion did rake up one of the highest numbers of victories, even though he only fought in the last 50-60 years or so of the Crusade. To me this coupled with the fact that the Lion was a known tactical genius would suggest they must have been quite adapt at almost any given fight as to get that many victories in that space of time would mean they would have to conquer any world they should come across quickly no matter what the enemies type or speciality. So i would say (imo, by no means fact) the Dark Angels would be specialists at adapting to any battle situation and to employ the most brilliant and well planned out tactics and strategies courtesy of The Lion
Emperors Children - Now the Emperors children strived for perfection in all kinds of warfare, but they were quite a small legion so would never be able to rake up the victories of other legions. But as they would strive for perfection in every way, coupled with their small numbers i would say they would go for tough planets to crack, fights that may take a while, be difficult and costly in man power, but with the Emperors Children perfection aspect i would say they would be able to beat these tougher enemies, in a shorter amount of time and minimise casualties all the while. The Cleansing of Laeren being a key example.
Iron Warriors - Seige specialists through and through, also being experts in engineering, aswell as garrison troops. Notorious for being able to break any defence, keep, fortress etc. Taking a very cold approach to warfare and being extremely ruthless. Used as garrison troops, overseeing compliances aswell. 10 Iron Warriors were enough to keep an unlucky population of 130 million.
White Scars - Experts in fast attack and hit and run tactics. Making heavy use of fast transport such as bikes and speeders.
Space Wolves - Close combat specialists. Fearsome and almost unstoppable when in an assault although still tactically sound unlike the World Eaters who are not so much, still noble however and did care about the human element.
Imperial Fists - Siege Specialists again, though argueably more dedicated to the defensive side of a siege, able to build fortifications that are nigh on impregnable, although they were still incredibly skilled at laying sieges aswell. All Companies followed a strict organisational structure and using a rigid system aswell as their skills in assaulting any position to rake up the second highest number of victories. Later became the Praetorians of the Imperial Palace on Terra.
Night Lords - Terro tactics. Used fear as a weapon as much as their bolters and equipment. The Legion was full of murderers, rapists etc, and as a result their terror tactics went to the extremes, wiping out entire planets if they resisted not stopping even if they surrendered. This led to them gaining a terror inspiring reputation, with some worlds surrendering the moment they found out the Night Lords were on there way.
Blood Angels - Close combat specialists, even before the flaw manifested. Shock troopers of the highest degree, even rivaling the World Eaters, although again like the Space Wolves would not descend to the level of the World Eaters. None the less they were still excellent in close combat. Also served as the Emperors personal guard, accompanying him when he still led the crusade.
Iron Hands - Experts with engineering and mechanics in general with a heavy affinity for bionics. Had close ties with the Ad-Mech. Eschewed the use of Chaplains, using Iron Fathers instead which fulfilling the role of techmarines and Chaplains. Known to be very blunt and straight forwards, not using more elaborate tactics and flare, depsired weakness.
World Eaters - Close combat specialists. Extremely violent and alltogether terrifying to behold, used pysco surgery and implants to increase their range and bloodlust, entirely ruthless in an insult, not even stopping to spare civilians or innocents, would slaughter an entire world to bring 'compliance' Again like the Night Lords some planets would rather surrender once they found out they would be facing the World Eaters.
Ultramarines - Tactical and Strategic brilliance due to the abilities of Roboute Guilliman. Stuck to a strict discipline, tactics and stratagems, some would view them as unimaginative and stuck up, but their victory laurels and accolades spoke for themselves.
Death Guard - Relentless and blunt assaults. Another legion which forwent the use of elaborate and stylised tactics. Extreme resilience to poisons and viruses(ahh the irony) and generaly resiliant in all other regards. Often used to conduct ship assaults and close quarter situations. Heavy use of infantry, not using armour or jump packs often.
Thousand Sons - Psykers through and through. Used their great psychic abilities to outwit and defeat their foes. Also extremely learned and knowlegable. Weren't fond of close combat.
Luna Wolves - Speartip assaults. Often employed the speartip tactic, using drop pods and assault craft to launch directly at the heart of the enemy, effectively dicapitating the enemy as it eliminated its leaders and command structure. Still highly flexible though with Horus in command, amassing the highest number of victories of all the Legions.
Word Bearers - Faith you could say. At first they would completely eliminate all resistance on the planet until the population was completely subdued, they would then go on to enforce the Imperial faith and convince the population of the Emperors divinity, making the most compliant worlds in the Imperium. However after being chastised by the Emperor they then went on to ruthlessly eliminate all resistance on a planet and then the rest for good measure, completely eliminating the planets resistance and often its population too. This led them to gain mroe victories than all the other legions in the closing years of the heresy (not total number)
Salamanders - Close quarter firefights and skilled artificers. Made heavy use of melta and flame weaponry much like their fiery homeworld itself. All the members of the legion were skilled artificers, able to craft their own weaponry, maintain and improve upon their armour.
Raven Guard - Guerilla warfare and stealth experts. Made extensive use of lightning attacks and warfare, striking at the enemies weak points and crippling them before swiftly crushing them. Able to operate effectivle behind enemy lines and have its commanders operate independently with a large degree of autonomy.
Alpha Legion - Infiltration, Covert Ops and Stealth specialists. Made extensive use of infiltration and cults, recruiting members of Imperial forces and others as operatives to work in secret for them. Would infiltrate the enemy and disrupt them as much as possible to sow confusion and weaken them greatly, also using a large amount of misdirection, only striking once victory is completely assured, leading to total victories with the minimum of casualties. Encouraged free thinking and a loose command structure, encouraging members of the Legion to voice their own opinions, make their own strategies and plans.