Hello,
In regards to the physical aspect, the entry fitness requirements are available on our website. If you were thinking of joining as a CMT the requirement is - mid thigh pull 46kg, medicine ball throw 3.1m, 2km run in 11min 15 seconds. More information on the fitness tests can be found here https://apply.army.mod.uk/how-to-join/can-i-join/fitness/physical-entry-standards
I wouldn't worry about achieving anything over and above the entry requirements to start with (although if you are already fit that can be a bonus). Phase 1 training is designed to build soldiers up gradually until they meet the Army standard, I would be cautious about going from doing very little to do doing too much before you start training as this can lead to injury. The Army website has information on how to prepare appropriately and they have an App you can download to help you (100% Army Fit App).
In regards to being mentally strong enough, that is only something you can answer. I found the application process quite useful, you get to experience the Army environment and it gives you an idea if that's an environment you could work in. Phase 1 training will gradually push your limits, both physically and mentally, and you will learn a lot about what you are capable of. Lots of people surprise themselves by what they can cope with.
I hope that helps answer your question.
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