This achievement is currently glitched for some. If you didn't unlock the achievement for the first reward of the gods, you will not unlock this one either. Even if you did unlock the first achievement, this one can still glitch. I don't know how widespread the issue is or what causes it.
As of a recent patch, Round-to-Round does work to unlock this. At launch, it did not. Let me know if this changes again.
You can do this solo.
To track this, when you're selecting your god you can see a little progress bar on the right side of the screen. It takes 10 "rounds" to get this. That means either 10 solo/round-to-round rounds or 10 arena rounds (which are actually 2-3 rounds, you get credit for one round for each full arena). Thus, solo is the clear way to do this.
You do need to actually complete the round. You can't start it and immediately die. That won't work.
To maximize XP, I'd recommend trying to wait until the other player selects his god, and then pick either Jupiter or Apollo to make sure you can get one of the time slowing focus powers.
EDIT: Since there is some confusion, you do, in fact, need to unlock all the rewards of the gods and so you need to do 40 rounds total.
The Gods and Their Weapons and Shields (Courtesy of Gizmo2k)
Execution: Focus Gain
Focus Ability: Time Storm (Slow Nearby Enemies)
Reward: Sword - Thunder of Jupiter (Crowd Bonus +2%, XP Gain +2%, Focus Gain +20%)
Mars THIS IS THE BEST ONE. GET IT FIRST. USE IT TIL LEVEL 45/90.
Execution: Damage Bonus
Focus Ability: Fires of War (Damage Nearby Enemies)
Reward: Sword - Measure of Mars (Focus Gain +30%, Focus Time +15%)
Execution: Health Regain
Focus Ability: Solar Stun (Slow Nearby Enemies)
Reward: Shield - Strength of Apollo (Crowd Bonus +1%, XP Gain +1%, Health Capsules +1, Inventory +1)
BETTER THAN DIANA. XP REFERRED TO DOES NOT HELP YOU LEVEL, IT'S DIFFERENT
Execution: XP Boost
Focus Ability: Hurricane Blast (Push Back Nearby Enemies)
Reward: Shield - Canopy of Diana (XP Gain +4%, Inventory 3 slots in total)