Damage or effects from another Creature
Sword of Answering (DMG):
Using your reaction to attack with a Sword of Answering, if the invulnerable creature damages you in range.
You gain a +3 bonus to attack and damage rolls made with this sword. In addition, while you hold the sword, you can use your reaction to make one melee attack with it against any creature in your reach that deals damage to you. You have advantage on the attack roll, and any damage dealt with this special attack ignores any damage immunity or resistance the target has.
Shadow's Strength Drain:
RAW: Even if a Shadow's Strength drain deals no damage to the invulnerable creature, its strength score will still be reduced. If its strength is reduced to 0, it dies.
Strength Drain. Melee Weapon Attack: +4 to hit, reach 5 ft., one creature. Hit: 9 (2d6 + 2) necrotic damage, and the target's Strength score is reduced by 1d4. The target dies if this reduces its Strength to 0.
Power Word Kill:
If the invulnerable creature has 100 or less hit points, the invulnerable creature will die.
You utter a word of power that can compel one creature you can see within range to die instantly. If the creature you choose has 100 hit points or fewer, it dies.
You can wish for the creature to die, to be taken to 0 hp, cast Power Word Kill, etc.
Aura of the Guardian (XGtE):
If an Oath of Redemption paladin is under the effect of invulnerability, and uses Oath of Redemption to take damage for another creature, the damage the paladin takes cannot be reduced.
When a creature within 10 feet of you takes damage, you can use your reaction to magically take that damage, instead of that creature taking it. This feature doesn't transfer any other effects that might accompany the damage, and this damage can't be reduced in any way.
If an evocation wizard uses their overchannel ability, they can deal damage to themselves, even under the effects of Invulnerability.
Starting at 14th level, you can increase the power of your simpler spells. When you cast a wizard spell of 1st through 5th level that deals damage, you can deal maximum damage with that spell.
The first time you do so, you suffer no adverse effect. If you use this feature again before you finish a long rest, you take 2d12 necrotic damage for each level of the spell, immediately after you cast it. Each time you use this feature again before finishing a long rest, the necrotic damage per spell level increases by 1d12. This damage ignores resistance and immunity.
Environmental or Other Effects
When a creature runs out of breath and cannot breathe, its hit points are reduced to 0.
A creature can hold its breath for a number of minutes equal to 1 + its Constitution modifier (minimum of 30 seconds).
When a creature runs out of breath or is choking, it can survive for a number of rounds equal to its Constitution modifier (minimum of 1 round). At the start of its next turn, it drops to 0 hit points and is dying, and it can't regain hit points or be stabilized until it can breathe again.
Maximum Hit Point Reduction
If the maximum hit points of the invulnerable creature were reduced below its current hit points, its current hit points would lower to match its new maximum hp.
This can happen when a spell that was increasing the creatures maximum
hp ends; or from a disease, such as Chaos Phage from a Blue Slaad.