I almost gave up on this level, until I discovered the single secret which turned 100+ failures in a row to a failure rate of only 50%!

After that, I restarted the game until I got one of these 4 relics:

• A Pair of Golden Lions
• Grugnir, Odin's Spear
• Hera's Thundercloud Shawl
• Pygmalion's Statue

Then it was only a matter of time.