Sure, I can suggest some phones under 20k that are good for gaming and have a good battery life but may not have the best camera.
1. POCO X3 Pro - This phone has a powerful Qualcomm Snapdragon 860 processor that is great for gaming. It also has a large 5,160mAh battery that can last you through the day. The camera is decent but not the best.
2. Realme 7 Pro - This phone has a Snapdragon 720G processor which is also good for gaming. It has a 4,500mAh battery with 65W fast charging. The camera is good with a 64MP primary sensor.
3. Redmi Note 10 Pro Max - This phone has a Snapdragon 732G processor which is good for gaming. It has a large 5,020mAh battery that can last you through the day. The camera is decent with a 108MP primary sensor.
4. Samsung Galaxy M32 - This phone has a Mediatek Helio G80 processor which is good for gaming. It has a massive 6,000mAh battery with 25W fast charging. The camera is average with a 64MP primary sensor.
5. Nokia G20 - This phone has a Mediatek Helio G35 processor which is decent for gaming. It has a large 5,050mAh battery that can last you through the day. The camera is average with a 48MP primary sensor.
These are some of the phones under 20k that are good for gaming and have a good battery life but may not have the best camera. Keep in mind that there may be other factors that you need to consider before making a final decision, such as display quality, storage, and RAM.