I think I know why you get this message after beating the SNES' Gradius 3 hidden arcade (balls hard) difficulty mode:
You see, the Arcade Gradius 3 was insanely hard. So hard that coins only worked to start the game, but not to continue... because it didn't even have continues. There were two releases in Japan: the first one had a "beginner mode" that let you play 3 levels, and a "normal" mode which had all the levels.
The second release removed those options and only gave you "normal" (A.K.A. insane) mode. The game received a limited release outside Asia (no USA version though), but it was based on the 2nd Japanese version that didn't have the difficulty select menu. And thus, that menu and what it said was lost to the ages. That is until the Playstation 2 release of Gradius 3 & 4. The version included was based on the 1st Arcade release, and Konami even translated all the menus.
As you can see, the "normal" mode is called "Technical Course" (Japanese version was called "technical Normal"), and it's obvious that's what the SNES version was referencing. "I'm give up. Your appellation's: Technical Monkey" in non-engrish should be "I give up. Your title is: Technical Monkey". I don't know what they mean by 'monkey', but 'technical' definitely comes from the Arcade difficulty selection screen.