"Aegis X
All attacks made against this object subtract X attack dice before rolling" - rulebook
"Bashed
When a creature is Pushed into a wall with the Passage Blocked trait it is
Bashed. It receives an Unavoidable attack of 3 attack dice of damage." - rulebook
Drain Life is not an attack spell, so Aegis does nothing against it.
Wall bashing is considered an attack, so Aegis would work against it.
Rule of thumb: As long as the attack is a dice attack and NOT the result of an enchantment or incantation, Aegis applies.
Just FYI, Aegis doesn't stack, and the attacker will never roll less than 1 die against Aegis.