You say two tetra died? This is probably causing stress on the tetra who are in turn taking it out on the betta. Tetra are schooling fish and need large groups. Six is the bare minimum that should be together. Getting more will help. Adding more cover will certainly help, too. Your tank does look a little sparse. Floating plants (fake or real) will offer both the betta and the tetra some good cover and will go a long way to make them both feel better.
EDIT: I also forgot to mention that decreasing light will do a lot to reduce the algae in a tank. The light shouldn't be on more than 10 hours a day and should always be off at night. Fish need a day/night cycle just like we do.