It is possible to obtain this very rare cyber elf, but I didn't say it was easy. Play through Hard Mode and collect (as well as power up to the max) every cyber elf, as well as getting Ranking A or S on every mission. If you start a new game from that saved game, you'll begin with every cyber elf, including Jackson.
After completing the game and saving when the game prompts you to do so, hold A when the credits appear when you complete the game any other time. Note: You must have at least one save with a ''1'' or higher to the right of your total play time.
After completing the game, you can start a new game in Hard Mode by holding the left shoulder button down while starting a new file. In Hard Mode, weapons do not gain levels, and bosses have new attacks.
Once getting passed the challenge of getting Jackson, Ultimate Mode is a bit easier to unlock. Simply hold R when selecting a new game after playing through Jackson Mode and using every cyber elf to play Ultimate Mode. Though the name suggests otherwise, this mode allows you to start with all of your weapons maxed out and with the effects of cyber elves already in place; permanent cyber elves no longer effect ranking. Also, you can now perform any of Zero's charged attacks without actually charging them. To fire a semi-charged Z-Buster shot, press Down to Forward + B (doing this combination with the Z-Shield equipped will use a charged Z-Shield throw). To perform a charged Z-Buster shot, press Down to Forward, Down to Forward + B. To perform a charged Z-Sabre slash, press Forward to Down + B. To perform a charged Z-Rod swing, press Forward, Down, Down-Forward + B.