How hard would it be to get to level 1000 under unmodded means?
You'd need to collect 4,339,720 XP to reach level 1000*; for comparison, the most XP that I've collected in any world is 3,920,679 and I've spent 143.18 real-time days on it (this is after I made my mod which separately tracks your lifetime XP; another world with 22.46 days of playtime resulted in a total of 708,515 XP accumulated; more recently, I accumulated XP at the rate of over 6,000 per play session over a one week period of caving, which included an average of 3,300 ores mined and 432 hostile mobs killed per day, which could be seen as the high-end of "legit" XP gain (without the use of farms). Of course, I've never gotten much higher than level 70 (aside from killing the Ender Dragon, which gives 78 levels in 1.6.4 but only 68 since 1.8#)
*Formula (for level 30+) = 4.5 * level^2 - 162.5 * level + 2220 = XP required to reach level
#Prior to 1.8 you only need 3,350,720 XP to reach level 1000 (3.5 * level^2 - 151.5 * level + 2220)