Step 1: Normal fatty acid breakdown happens through beta oxidation, which removes two carbon units at a time by acting on the beta carbon, the third carbon from the carboxyl end.
Step 2: Phytanic acid has a methyl branch sitting exactly at that beta carbon position, and this branching blocks the enzyme machinery of beta oxidation from working directly on it.
Step 3: To get around this block, the cell first performs alpha oxidation, which removes a single carbon from the carboxyl end and repositions the methyl branch so that the molecule can subsequently proceed through normal beta oxidation.