There's no possible way Tetra is getting in alone, so let me make it clear what my suggestion is. I'll also message the OP with a full move set I thought of for Tetra then.
Make her the main character, but have Toon Zelda available. Meaning two things.
1. It's her final smash that transforms her into Toon Zelda.
I see it like this. Tetra hits the smash ball with a flip kick attack that's her in air up A move. She gains the power of the Smash Ball, and lands on a platform with Mario and Yoshi on it.
Upon activating the smash, it zooms in on Tetra's hand glowing, and a giant yellow explosion in the form of the triforce takes over, sending away anyone near it out of the arena. Thus, making her Toon Zelda.
To get her back into Tetra? Nothing too special. Toon Zelda gets the smash ball, and the same effect happens.
Or, you make her the down B move. I'm totally in support of Tetra making it in, and I feel she's COMPLETELY deserving of it. More so than most other characters mentioned.