You need around 205.000XP for level 25. I got it during chapter 8 in Moresby, act II. I played around 15 hours to get to level 25.
Just play through all quests you can find and do not rush through the game. Use the rage ability in crowded areas like the streets of Moresby where you can find up to nearly 10 zombies gathering around, the multiplier is giving you good XP. Take your time to enjoy and explore Dead Island.