Sorry for a late reply, but you can use something similar to the following:
{
"Version": "2012-10-17",
"Id": "Policy1459542796200",
"Statement": [
{
"Sid": "Stmt1459542791970",
"Effect": "Allow",
"Principal": {
"AWS": "arn:aws:iam::123456789:user/mybackupuser"
},
"Action": "s3:*",
"Resource": "arn:aws:s3:::mybucket/*"
},
{
"Sid": "Stmt1459542791970",
"Effect": "Allow",
"Principal": {
"AWS": "arn:aws:iam::123456789:user/mybackupuser"
},
"Action": "s3:ListBucket",
"Resource": "arn:aws:s3:::mybucket"
}
]
}