Being hit with explosion has a 33% chance to destroy the trinket and spawn a Coin, a Heart, a Key and another trinket. The pickups may be of any normal variety.
Notes
Taking damage from the explosion is not required to trigger the effect. This makes effects granting Invulnerability very useful for safely destroying the Walnut.
Getting hit by multiple explosions simultaneously has a high chance of cracking the Walnut, as every individual explosion will have its chance to activate the effect, no matter how closely they occur.
Synergies
Bomber Boy: As Bomber Boy causes 9 explosions at once, laying a bomb and not moving before it explodes is almost guaranteed to trigger the trinket.
Gnawed Leaf: Isaac will not be knocked back from the explosions, but it will count for the trinket.
Holy Mantle: Explosions hitting the mantle still count for the trinket.
Host Hat / Pyromaniac: Isaac becomes immune to explosions, which allows to get the effect without any risk.
Coin, a 
Heart, a 
Key and another trinket. The pickups may be of any normal variety.
Bomber Boy: As Bomber Boy causes 9 explosions at once, laying a bomb and not moving before it explodes is almost guaranteed to trigger the trinket.
Gnawed Leaf: Isaac will not be knocked back from the explosions, but it will count for the trinket.
Holy Mantle: Explosions hitting the mantle still count for the trinket.
Host Hat / 
Pyromaniac: Isaac becomes immune to explosions, which allows to get the effect without any risk.
The Binding of Isaac: Rebirth
