Polybius has five parts:

1. Assault challenge.  Use fairy + sceptre on jester if solo or duo (split up).  EV can fly to north core.  In large groups hero boost and cat can help.
2. Tower defense.  Traps are optional, and you can usually get away with just archer-spider-mage-archer.  The boss fight area at south is for the next wave.  To avoid djinn unsummoning, don't go south or upgrade there until the wave is nearly over.
3. Kraken battle.  Use a seahorse + monk.  In groups, bring a cat.
4. Puzzle.  Skip this by flying with summoner, and build an orc minion at the spot shown to get the proper height to fly over the spikes before the door.
5. Boss battle.  Use your favorite DPS hero.  EV, Jester, Monk, and Barb can all solo it, but EV is probably bet.  In groups, hero boost and cat will help a lot.

Tips for the boss battle:

1. Web + fire = death.  Activate the pylons and kill the demon lord / goblin mech first to remove fire from the equation.  After this, you can safely beam the spider queen.  The spider queen goes into vulnerable mode when her baby spiders are dead.  DO NOT forget to kill her remaining baby spiders after she's dead.
2. Kraken is last.  EV beam doesn't work on the kraken at all, and rainmaker is good on the body but useless against tentacles.  Sceptre works well on both.  Once the tentacles are dead, kite the kraken from pylon to pylon in preparation for the next phase.  You can only damage the body from the front, not the sides or back. 
3. Beam the turkey while the pylons are up.  Don't get hit by the Mega Turkey's shockwaves.  Unless you're very fast, try to cancel hero boost during the previous phase so you can start it in time for the turkey battle, right when you shoot the last pylon.
4. The four evil heroes can heal to full if you leave them alone, so try to focus on one hero at a time.
5. The evil apprentice has a mana bomb which one-shots the entire map.  It takes 60 seconds to charge.  If you bring Jester, make sure you have a 100% block sword, and 60 seconds after you hear the charge sound effect, face the apprentice and block.  If you bring monk or EV, kill the apprentice quickly, especially if you hear it charge.
6. Zooming out can help with visibility and reliably aiming vs ninja; just watch for the blue of the ninja's weapon, and track it with your eye and mouse.  If you zoom out, make sure you have a binding for rotate camera (default is ctrl, I put it on a mouse button).

Good luck :)

This is a solo video, but it's faster and easier in a group.

Routes for assault portion: