Had this song bookmarked for a number of months so that I completely forgot about what it was all about aside from the title "Dream Shift".
I found out, or to be more accurate, I was reminded that "Dream Shift" was the opening theme for "Zettai Muteki Raijin-Oh"（絶対無敵ライジンオー...Matchless Raijin-Oh）, which, according to Wikipedia, was one of those landmark anime that launched the premise of young kids manning their own mecha to save the world. I was kinda surprised that this premise hadn't started earlier because this sounds like something that has been in Japanese kid culture for decades, but perhaps this was more prevalent in the tokusatsu shows of the 1970s. In any case, try to imagine a callow kid from Tatooine taking on a planet-killing battle station and actually winning.
It was awfully hard to find out anything about "Dream Shift" and its singer aside from the fact that it was listed as such on the J-Wiki article for "Zettai Muteki Raijin-Oh". However, I managed to glean the information that it was sung by a vocalist for the band Silk at the time who had started show business in the mid-1980s as Kinuko Ohmori（大森絹子）; incidentally, that first kanji in her first name actually means "silk". Apparently, she debuted with the opening theme song, "Kon'ya wa Hurricane"（今夜はハリケーン...Tonight is a Hurricane）, for another well-known anime from those days, "Bubblegum Crisis".
Ohmori then got Silk together in 1991, the same year when "Raijin-Oh" debuted on TV screens. I can imagine the kids getting really revved up at the start of each episode with "Dream Shift". It's pretty nostalgic for me, too, since Ohmori sang like a number of other female pop singers at the time: lots of gushing enthusiasm backed up by a dynamic guitar pop-rock melody. When I first heard the song, I immediately thought Misato Watanabe（渡辺美里）, but then there were other big-voiced singers at the time contributing their wares to anime such as Mariko Nagai（永井真理子）and Miho Morikawa（森川美穂）.
"Dream Shift" was written by Hitoshi Shinohara（篠原仁志）and composed by Kazuya Izumi（和泉一弥）. As for Ohmori, she would retire in 1994. To finish off, I leave you with this scene of what must be the world's coolest public school.
P.S. I found the translations for the lyrics here.