Leveling up in this game is kind of complicated. It's not just a simple system of get a kill, get a certain amount of XP.
First of all, you must be wearing unmastered gear, preferrably in all slots. Your bear only gains the XP that the gear gains, so if you gained something like 2,000 XP in a level but only had one unmastered item and it only needed 50 XP to become mastered, you will only gain 50 XP. If, however, you were wearing all high-level gear that was unmastered and had 0 XP each, you'd be gaining 10,000 XP (5 pieces of gear * 2000 XP). So make sure you're always switching gear as stuff gets mastered, or you will be wasting time and XP.
The XP system doesn't make a whole lot of sense to me. It's some kind of derivation of your level score, but I don't really understand the math used. It's not just remove a few zeroes, like if you had 250,000 level score, you'll get 2,500 XP or anything simple like that. This makes it hard to pinpoint exact spots to grind for exact gear, so I think the best idea is to simply switch it up constantly as you play, making sure you never carry unmastered gear. This is going to be a pain in some levels, because some of the gear actually makes your character worse, not better. Obviously, you'll want to do an early level or two for those items, while saving high-level gear for later levels.
Keep in mind that, for example, running straight for the target bear and leaving won't get you much XP, as every enemy in a level will give you the same amount of points regardless of what you do them, except some enemies will randomly have a higher kill value than others. For example, the hidden temple enemies give you 10,000 points. The problem with that is that 10,000 points is nothing and will not get you very much XP, so the only viable method is to clear entire levels and score high-level trophies, meaning you'll end up doing entire 15 minute runs just to master one item of each type.
The best way to make sure you're gaining as much XP as possible for your gear is to go into a level and score as much points as possible. In that regard, using later levels probably won't be as efficient as using middle levels, as the last few levels are obviously harder, take longer and don't yield as many points per minute.
In my opinion, the best two levels for easy points are Oodoo (level 33) and Giggles (level 15), Oodoo for the sheer number of enemies and Giggles for how curiously easy it is to rack up very high scores on it. My high score on that level is like 100,000 over the platinum limit and the level is not difficult at all unless you're wearing very bad gear.
Remember to always leave a level instead of quitting or restarting! Doing the latter two will not let you keep any items or XP, but leaving will give you the amount of XP you've gained with no punishment. Dying, however, comes with a severe punishment, so if you've gotten a good amount of XP but aren't feeling good about your situation - maybe you've stolen a stupid costume that gives you horrible stats and every other bear is aggro'd against you - just leave the level instead of taking the unnecessary risk.
Expect a grind, as this will not come naturally through game progress. The platinums are very easy to obtain and you'll be grinding XP and item mastery for long after you've killed every target and scored every platinum. There is currently no known method for fast, efficient XP gain besides what I've posted here.