There are basically 2 types of backups you can use.
a) ASE backup
b) O/S level backups.
To improve ASE backup speeds, you can probably look into striping the database backups.
In sites where there are very large databases (VLDB), clients look into O/S level backups since they can be considerably faster. For eg., a EMC backup of Gigabytes of data can take just a few minutes.
In earlier versions of Sybase, in order to do a O/S level backup of your database, Sybase requires you to shutdown the ASE Server to preserve data integrity. This was a tedious process.
In 12.5 version (please check exact version this was introduced), quiesce database is introduced by ASE, which will enable you to take O/S level backups without shutting down the ASE server. Please read up on "quiesce database" command.
If you are looking into Option b, please do look into the pros and cons before taking up this strategy.
And definitely TEST TEST TEST before implementing it in PRODUCTION.