Entry needs a Dungeon Key plus a Yul fee. Rewards are reported to shrink when you heavily out-level the tier.
Beating the wave-5 boss is not the end of the run — check the wave counter before leaving.
Save cooldowns for boss waves; the waves before them drain mana.
Where Boss Keys come from
Boss Keys are spent in the Boss Summon interface on Colosseum Island. They come from codes (TREASURE10K, TREASURE20K and FIGHTON all paid one before expiring) and appear in Dungeon boss loot. Check the current list on the codes page.