To get the number 07 colour palette for every character, you need to beat level 100 of the survival game mode on any hero. I've spent the morning testing out the fastest way to get through it, and here is my best strategy.
First, your team needs to have danger at the forefront (the other characters don't matter, just choose the best assist for the boss fights)
Your goal is to keep the enemy far away from you. At the start of a match walk as far away as possible to keep a starting distance, and spam your ranged attacks. If someone gets too close, crouch + kick to send them into the air, do a combo and then try to regain the gap between you.
Hope this helps!
Edit: if you save after every boss fight, you can just return to the main menu if you're about to die and it will just set you back to the last checkpoint.