1
I apologised my friend for forgetting her birthday.
I apologised to my friend for forgetting her birthday.
Use apologise to + person to say who receives the apology: ‘I apologised to my friend.’
2
I apologised to breaking her phone.
I apologised for breaking her phone.
Use apologise for + noun/-ing to say why you are sorry: ‘I apologised for my mistake.’ ‘I apologised for being late.’
See SORRY