How do I increase the amount of tuition I am claiming this year? I have around $4000 of federal credits moving to next year but still have a $300 balance due.

There may be another reason for the balance due. If you're self-employed for example, your CPP contributions due can't be wiped out by tuition.

Take a look at the Detailed Tax Summary to determine if you have other amounts due that cannot be lower by non-refundable credits like tuition. If line 420 has an amount other than zero, return to the Student section of your return to ensure the tuition has been entered properly.