Pretty straightforward - reach lvl 15 to unlock Ranked 1v1 Duels and kill your opponent once to fulfil the "be the only God still alive on the map" condition that way.

There are a few potential downsides to this method, mainly:
- Queue times, especially in low population regions. For example, I couldn't get a single match after 20+ minutes of waiting on the OCE server.
- You have to reach lvl 15 before you can access the gamemode.
- It relies on you actually getting a kill in PvP.

Can be easily done with bots:

1. Start a 3v3 Joust match with Medium AI.
Easy bots are too stupid, and for this achievement you need the enemy to actually be able to kill your teammate bots too.

2. (Optional) Pick a character able to kill gods quickly.
The respawn timers will lengthen the longer the match goes on, so you can really do it with any attacker character. Personally, I did it on the default build Hades with Blink in about 7 minutes.

3. Be greedy and selfish.
Grow strong at the expense of your team. Simply farm minions at the beginning and try to finish your first few items as quickly as possible. While you grab the jungle monsters, the enemy will push the wave towards your tower. So unless you get really unlucky with the team compositions, your bots should be outmatched in a 2v3 and not put up much of a fight.

4. Look for the right moment in which all three enemy gods are gathered for a tower push and kill your two bots.
For me it happened right after they destroyed my first tower. As soon as it happens you will have, depending on how long the match has been going, about 20-30 seconds to wipe out the enemy team.

If you picked Hades, use Blink to get in the middle of the enemy team. Medium bots are still dumb and slow, so you will have plenty of time to find the right spot to cast your 4, hopefully drawing all three enemy gods into the vortex. Cast 3 during the vortex to proc the explosion and then use 1 to chase down any survivors.