So far, we know that you can only earn titles and resting area bonuses. There doesn't seem to be any achievements related to the daily reward system. I can assure you there is nothing additional besides-
Earning Titles (which are just to show off to others, and won't give you anything additional other than motivation to get a certain title):
- Creature of Habit (Grade 1): Reward Streak of at least 7 days of consecutive logins.
- Creature of Habit (Grade 2): Reward Streak of at least 30 days of consecutive logins.
- Creature of Habit (Grade 3): Reward Streak of at least 90 days of consecutive logins.
- Creature of Habit (Grade 4): Reward Streak of at least 180 days of consecutive logins.
- Creature of Habit (Grade 5): Reward Streak of at least 365 days of consecutive logins.
Source (Tibia Fandom) Cyclopedia
Picking up your reward on a daily basis increases the counter of your reward streak. As your streak grows, you gain access to special bonuses in addition to your rewards. The bonuses are unlocked during the first 3 (Free Accounts) or 7 (Premium Accounts) consecutive days of taking rewards and stack with each other, staying available until your reward streak is reset. These streak bonuses are applied when the character is inside a Resting Areas and are the following:
- No bonus for the first day.
- Allow hitpoints regeneration
- Allow mana regeneration
- Stamina regeneration (Premium only)
- Double hitpoints regeneration (Premium only)
- Double mana regeneration (Premium only)
- Soul Points regeneration (Premium only)
Source (Tibia Fandom) Daily Reward System
I'm currently at 1825 days, which is 5 years.