Floor 39 is the thirty-ninth level in Heavenly Tower.
At about 10 seconds an Elder Sloth will spawn. Roughly 20 seconds later, the boss, Codename "Red Riding" comes out, followed immediately by a Mr. Mole. A few seconds later the first Tackey spawns, followed later by more Mr. Moles and Tackeys. Up to 4 Mr. Moles and up to 4 Tackeys each will spawn. After the final Tackey, no other enemies will spawn.
The key to this stage is speed. Bring units that are as fast as possible, to sneak through the blind spots of Red Riding, Tackey and Mr. Mole. Manic Lion is a good cat on this level and so are Awakened Bahamut, Bullet Train and, especially, Green Shell. Spawning Manic Lions as quickly as possible can overwhelm the Elder Sloth, leaving the rest of the enemies vulnerable to their own blind spots.
Remember to time your units well so Red Riding doesn't snipe them. Sniper the Cat can be very useful on this stage as he can control the distance of the enemies on the battlefield.
Strategy 1 (ft. Yukimura)
Lineup: Two worker Cat level up Catcombos, or 2 attack up catcombos, Manic Lion Cat, Maglev Cat, Awakened Bahamut, Immortal Yukimura, Catellite.
Rush the Elder Sloth with Catellite. After it dies, purely rush the enemy with all the line 2 units.
If you don't have these units, just use other rushers or tanky that resist knockback.