This is a complete list of Matrix Supergirl's appearances from her 1988 debut to the 1996 SUPERGIRL series, taken from The Grand Comic Book Database and the partial listing at The Unofficial Supergirl Chronology. Dates shown are the cover date, which is two months ahead of the release date.
In 1985 DC killed off Supergirl in Crisis on Infinite Earths #7. They had decided to return Superman's status as the sole survivor of Krypton. So important was this to them that it was decreed, at the conclusion of Crisis on Infinite Earths and later in the Superman reboot (Superman: Man of Steel 1-6 by John Byrne), that not only was Supergirl dead, but she had never existed in the new timeline. An insult to a great hero? You bet. And not a little misogynistic. The Post-Crisis revamping of the DC universe was a period of great backlash against female superheroes, and many were killed off, depowered, or had their origins radically altered to distance them from DC's male superheroes. DC would slowly reintroduce familiar elements of the Superman story in new forms, including a Superboy who was a clone of Superman and played a major role in the 1992-1993 Death and Return of Superman. But they showed extreme reluctance to reintroduce Supergirl in any form that might challenge Superman's supremacy.
In 1988, scarely three years after Kara-El's death and wiping from existence, DC ran a story called the Supergirl Saga which introduced a character who looked like and was called Supergirl, but was in fact a clone of another dimension's Lana Lang, artifically given superpowers and completely unrelated to Kal-El. This character became known as Matrix for her protoplasmic origins. Readers eagerly took Matrix to be the new Supergirl. DC resisted. In the Adventures of Superman #457 letter column, editor Mike Carlin insisted in response to two readers' letters that, in fact, Matrix was not the new Supergirl, and they did not even wish to call her Supergirl. Whaa? During the "Superman in Exile" storyarc, the shapeshifting Matrix took on the role of Clark Kent to protect the Kents, and was written out at the conclusion of that storyline.
DC's approach to the character evidently changed, because three years later Matrix would return in "Panic in the Sky" and take on the mantle of Supergirl for good. Unfortunately this promising turn of events was followed by an unpleasant Supergirl-Lex Luthor storyline in which Supergirl became a member of "Team Luthor" and essentially became Luthor's kept woman, constantly referred to as "Lexcorp's Supergirl" in her few, brief appearances during an otherwise interesting storyline (the Death and Return of Superman). The end to this distasteful storyline came in the 1994 SUPERGIRL miniseries; following it Supergirl became a member of the New Titans until 1995. Her appearances in that series are unremarkable. A new level of depth for Supergirl emerged in SHOWCASE '96 #8 (Sept 1996), written by Peter David as a prelude to the fourth series which debuted that same month.
Matrix Supergirl was a fairly one-dimensional character who only became a character in her own right when she was merged with Linda Danvers II, gaining a secret identity and becoming a lot more like the Supergirl one would expect: humanized, heroic, and with powers portrayed simply as super, not different or inferior to Superman's. Prior to Peter David's series, writers tended to define her in relation to male characters, primarily Superman and Lex Luthor. The potential for a real, living super woman was always there; it was just not recognized by male writers who were content to quickly sketch in the outline of a (purportedly heroic) woman before getting back to their real business of telling male heroes' stories. So while this appears to be a long list of Supergirl appearances, in most issues she is a minor character who does not have a large role to play. This makes her starring roles all the more precious.
Issues which are notable for Supergirl are available for download in CBR/CBZ format. A few issues just have the relevant pages which feature Supergirl and are unrelated to the issue's story; issues marked "N/A" are ones I don't have. The entire post-Crisis Superman continuity can be downloaded from Bit Torrent sites in a series of torrents called "Superbooks" #1 thru 6. Some issues can be purchased from Mile High Comics.
The debut of the second Supergirl was foreshadowed in small cameos for a number of months prior to the origin story in "The Supergirl Saga".
Following the three-part Supergirl story, Supergirl reverted to an androgynous form and began calling herself Matrix in the "Exile in Space" and "Superman on Earth" storyarcs. She initially appears very briefly in this form in the following four issues, which evolve into a B-plot wherein she impersonates Clark Kent while Superman was off in space. At the end of ACTION COMICS #644 Matrix left Earth just as Superman had previously done. It would be three years before DC brought her back. Note: you can download the full issues or just the pages featuring Matrix. The A-plot starring Superman is extremely dull; the scenes back on Earth are the only interesting part of the story in my opinion.
Matrix returned in ACTION COMICS #674 in 1992, initially in the form of Superman. She would play a pivotal role in the 8-issue "Panic in the Sky" storyline, returning to her original Supergirl form for good by the end of the story arc. Matrix/Supergirl is featured throughout the following issues.
Following the "Panic in the Sky" story, Supergirl began an alliance with Lex Luthor II, not realizing that he was in fact Lex Luthor in disguise, and not at all the person her Lex had been. During this two year period, Supergirl was reduced to being Lex's "kept woman", and most of her brief on-panel appearances have her draping herself and simpering over him, pointedly posing for the male audience's enjoyment >_< Few of these issues are worth reading for Supergirl, which is a real shame because they take place during the exciting Death & Rebirth of Superman storyline (starting with the "Doomsday" arc) that introduced four new "Supermen" who were all interesting and complex characters.
In 1994 DC Comics put out a "trial run" 4-issue Supergirl miniseries to see if there was support for an ongoing series. Evidently there was, because two years later the 1996 series debuted. Following the revelation that Lex Luthor II was in fact the real Lex Luthor and had been exploiting Supergirl all along, Supergirl's relationship with him came to an explosive end in this series.
*Reprinted in SUPERMAN: They Saved Luthor's Brain.