#1: Leia takes Luke swimming (Star Wars #15, 1978, by Archie Goodwin & Carmine Infantino)
At about the same time as this early comic the novel Splinter of the Mind's Eye asserted Leia couldn't swim - yet Luke, improbably, could! Here, Archie Goodwin demonstrated a better sense of who the characters were as Leia was quite adept at swimming (plenty of water visible on Alderaan) while Luke was not (not many oceans on Tatooine). This moment brought back the sense of Leia's superior skill during the cell block rescue in Star Wars and was an early indicator that the comic series would be all right under Goodwin's guidance.
#2: Leia the commando (Star Wars #30, 1979, by Archie Goodwin & Carmine Infantino)
In a later issue, Goodwin sent Leia on a commando mission to an Imperial world. Considering Han and Luke were not (at this point in the series) going on such missions, it said a lot about Leia's uber-competency. She was the Snake-Eyes of Star Wars! It's a pretty great story as Leia fails to achieve her mission's stated goals but considers it a success because her actions have inspired other citizens to resist the Empire.
#3: Leia outwits Darth Vader (Star Wars #48, 1981, by Larry Hama & Carmine Infantino)
Speaking of Snake-Eyes, Larry Hama wrote some Star Wars! In this tale, Leia is playing a very clever con game against Darth Vader himself. She does succeed at everything she sets after this time - although at the last moment Vader is able to claim a minor victory. Take note also that this issue demonstrates that, prequels notwithstanding, it is possible to derive drama from economics in the Star Wars universe.
#4: Leia compromises (Star Wars #55, 1982, by David Michelinie & Walter Simonson)
Leia was helping to establish a Rebel presence on the planet Arbra, an ideal new base of operations. However, the native inhabitants, the Hoojibs, objected to the Rebels walking in and displacing them from their home. While some of the Rebels are willing to go against the Hoojibs' wishes, Leia notes they lost their own homes to the Empire and shouldn't repeat the Imperials' mistakes. That willingness to withdraw is what finally changes the Hoojibs' minds as they invite the Rebels to remain as their guests (Hoojibs remained a constant presence in the series from then on).
#5: Leia takes out an Imperial base (Star Wars #65, 1982, by David Michelinie & Walter Simonson)
On another commando mission, Leia intended to sabotage an Imperial base's reactor. An Imperial officer who had recently suffered a demotion due to a previous failure against the Rebels succeeded in trapping Leia inside the base. The exits were seealed and the officer set the base's reactor into an overload, believing it best to ensure Leia's death as a crippling blow against the Rebellion. Unfortunately for that officer, even with all the doors sealed and the base about to explode, he underestimated Leia's skill as she effortlessly knocked him aside and escaped (this issue also has a great scene where Leia takes out a hapless Stormtrooper).
#6: Leia hunts the bounty hunters (Star Wars #68, 1983, by David Michelinie & Gene Day)
Simply seeing Leia in a pilot's uniform is a treat, but this tale, told in the year leading up to Return of the Jedi had Leia and C-3PO tracking the bounty hunter Dengar, which brought them up against Fenn Shysa, a Mandalorian warrior garbed exactly like Boba Fett, yet quite well-disposed towards the Rebellion. In issues after Jedi, Fenn would become a regular member of the series supporting cast and a new rival for Han to contend with over Leia's affections.
#7: Leia's best frenemy (Star Wars #73, 1983, by Jo Duffy & Ron Frenz)
There certainly aren't many women in the Star Wars universe, but Jo Duffy put a lot of effort into building up her character Dani the Zeltron, a man-chasing smuggler. By 80s comics standards, Dani was the Yukio to Leia's Storm. It made a difference to have Leia interact with another woman and this was the first of many instances where Leia would chaffe at Dani's over-enthusiastic friendship and questionable moral code. In this story, Leia and Dani wound up joining forces in an effort to retrieve the tapes of a missing Rebel pilot (a running sub-plot which ultimately led directly into Return of the Jedi).
#8: Alderaan, remembered (Star Wars #86, 1984, by Randy Stradley & Bob McLeod)
In this tale, Leia met a Stormtrooper who originally came from Alderaan and wore a piece of his homeworld's remains around his neck. Leia is disgusted with him for betraying their people's memory and much of the issue was comprised of Leia delivering pointed takedowns of the Stormtrooper's justifications.
#9: Leia brings down a Sith lord (Star Wars #88, 1984, by Jo Duffy & Bob McLeod)
The post-Return of the Jedi comics had to find a number of new enemies for the protagonists to face. Looming largest among them was Lumiya, a female apprentice of Vader's who assumed her former master's role and began exerting control over the Empire's remnants. But to Leia, Lumiya was just another punk and she won this first confrontation with a blaster shot to Lumiya's chest!
#10: Leia's dress (Star Wars #95, 1985, by Jo Duffy & Cynthia Martin)
Leia's distate for Zeltrons came up constantly and she wound up having four male Zeltrons assigned to her staff. The quartet were very well-meaning but rather vapid; here, they decided to help Leia's appearance at a formal function by altering her dress - under the apparent mistaken belief Leia was a cabaret singer. In spite of it all, Leia did her best to maintain her dignity.
I hope you enjoyed this list!