You can disable journal entry notifications (Instant Alerts) by going to Settings > Notification Preferences.
Under the "Notify me when clients..." section, unselect the phone icon next to "Post or comment on journal entries":
Limiting Notifications to Clients with Specific Tags
Optionally, you can limit the journal notifications you receive based on your clients' tags.
1) Click the button to the left of the phone icon to open the tag list popup:
2) Select the tags for clients you'd like to receive alerts for then click Done to close the popup.
3) Click Save Changes to save your notification preferences.