Allah is the most merciful and his mercy is infinite, so I really hope that Allah is able to accept this request of mine.
Absolutely you can ask for that, you can ask for anything you like as long as it's not something sinful.
Prophet Mohammed use to make a similar du'a =
اللَّهُمَّ اغْفِرْ لِي ذَنْبِي كُلَّهُ دِقَّهُ وَجِلَّهُ وَأَوَّلَهُ وَآخِرَهُ وَعَلاَنِيَتَهُ وَسِرَّهُ
Allahummaghfir li dhanbi kullahu, diqqahu wa jillahu, wa `awwalahu wa akhirahu, wa alaniyatahu wa sirrah
O Allah, forgive me all my sins, small and great, earliest and what is towards the end, open and secret.
This hadith found in [Sahih Muslim]
Now the question is, what will we do to earn his forgiveness? Obedience to Allah is the best way,
you may ask for that, you can ask for anything you like as long as it's not something sinful,not good or najaiz-o-haram.
But you also must have to decide that in future i wouldn't repeat the sin from your heart. For Allah Azwajal every thing is possible. Allah Azwajal says, ask me i will give you, ask for my mercy i will forgive you'r sin , but we have to made a promise to Allah Azwajal that we we'll never do that sin again.