* not pictured: Bloom at the Element Cube, playing the MMSF games and trying to find the first one's "savage bull", the second one's medals (Apollo Flame gone), the third one's Outer Astro Wave 1 seen and the fourth one dreamed about as a Final Fantasy crossover *

Taurus Fire SP can be found in Echo Ridge, though he only appears as a random encounter (use SearchEye so he'll be more likely to appear).
I haven't defeated Apollo Flame because I haven't gotten all 150 Standard cards in Star Force 2 yet. To get the medals, you need to have beaten the game, beaten Apollo Flame, gotten all Standard Cards, gotten all Mega Cards and all Giga Cards.
I hope to find all 3 Sigma Bosses and win against them. Sirius Σ is found in the Orbital Base, Apollo Flame Σ is found in Black Hole Server 2 and Moon Destroyer Σ is found in Noise Wave 3. Beating them gets you the Sigma Star, allowing you to find Crimson Dragon Σ in Outer Astro Wave 1/2. He's really tough so be careful.

I'm sure Bloom watched this already, but if she hasn't it's there for her now.