Learn how to take that big breath before you go underwater. You want to focus on activating the diaphragm, isolating the muscle then allow it to go into the chest. A follow along video that you can practice at home out of the water.
Start at the diaphragm by putting one hand on your stomach. At first, avoid using your chest. Practice breathing a few times with your diaphragm only and avoid putting the two muscle groups together.
Next, combine the diaphragm breathing with the chest. Start with your diaphragm breathing, pause for a second, now take the air up into the chest, pause then let it slowly out. Be sure you keep the two separated by placing your other hand on your diaphragm first then place your hand on your chest.
To maximize your breath hold, start with your inhale and bring the air in with your diaphragm first then go into the chest using your chest muscles. Do not put the two muscles together. Repeat this until you can keep the two muscles working independently. The volume of air you really need goes in using your diaphragm and the chest is your bonus.
Next, practice making it a fluid motion, diaphragm then chest. Be careful not to go back to the habit of only taking air into your chest. Practice this out of the water and notice how your bottom time will improve.