In order to get the ball rolling on this card, you need to equip it with something first (or otherwise boost its ATK). Otherwise, it will never deal any Battle Damage to get stronger in the first place. Once that's done, this card is entirely based on its long-term potential. To maximize that potential, use cards that would stop your opponent from attacking this card such as "Swords of Revealing Light", "Waboku", "Gravity Bind", and many more. If you keep attacking your opponent's Life Points (by using the effect) under the protection of "Swords of Revealing Light", for example, it will gain a significant amount of ATK to become a dangerous card to your foe and still have the ability to attack his/her Life Points directly. "Earthbound Immortal Chacu Challhua", while in Defense Position, will also prevent your opponent from attacking and will inflict burn damage each turn.
A good way of getting this card to activate its effect is with "Banner of Courage". Not only will it activate this card's effect, but also boost any other monsters you summon afterward.
Equipping this card with "Twin Swords of Flashing Light - Tryce" along with "Axe of Despair" will increase this card's ATK much faster. By the Standby Phase of the second turn after this monster attacks, it will be at 2500 ATK and be able to attack twice.
An interesting, and a seemingly more efficient way to use Mucus Yolk is to equip it with "Unstable Evolution", as it will cause its ATK to immediately rise to 2400 (should your Life Points be lower then your opponent's). However, it is not too much of a problem if your Life Points are higher, as this card will still have a decent 1000 ATK to go directly with, and will soon increase to 2000 if it attacks.
This card is almost outclassed by "Raging Flame Sprite", which starts at 100 ATK and is rewarded the boost right after it attacks. This card's only effective advantage is that its ATK increases even if its damage is dealt through battle with a monster. If you can trick a monster into rushing this card and stop the attack with "Negate Attack" or suchlike, you can crush the monster on your next turn and get a boost afterward.
A card that feeds off of the delay in this card's boost, such as "Bottomless Shifting Sand", can provide this card with some support if you don't let it stay out too long.
Use "The Seal of Orichalcos" to protect this card (by also having a stronger monster on your side of the field) and to give it the necessary ATK to begin using its effects.