So I recently restarted the game and want to reach level 4 by the end of White Orchard so I can get the Temerian Armor. I'm playing on death march difficulty and so far have been unable to reach level 4 after doing all the side quests (that I know of) and ? locations. I know most people can reach level 4 by the griffon fight but I can't seem to do it. Am I missing a quest? High level monsters to fight? Anything? Any tips would be appreciated and I'm sure make reaching level 37 by the end of the game easier as well. Thanks in advance.

Hi, there! Consider sending Geralt out, exploring the countryside. n_n
Can't you put drowners (lvl 4, IIRC) out of their misery? You should be able to find them along the river. Don't they respawn overnight?

Only side quests? By far the best source of XP is the main quest, followed by side quests, and monster hunting has the least. Try following the main quest line as well as side quests.

And use AXII whenever you have the chance to...

Yes but the goal is to be level 4 BEFORE advancing the main ques to Vizima.

You can easily get to level 4 before going to Vizima. Just do everything except talk to Vesemir after the griffin quest is done. Once you talk to him (after the griffin quest) you move on from White Orchard, so just do everything except that, and you will be level 4.

Do the griffin quest up to killing it, but do go an collect the reward. You want to get the thunderbolt potion and the crossbow.
Make sure you visit the huntsman before locating the griffin's nest (minor quest you will not get if you find the nest before speaking to the huntsman). Also, visit the herbalist for the xp you get for treating the girl the griffin injured.

The reason for getting the crossbow is that you should harvest about 15 pieces of buckthorn (for later use in potions and oils) and you can kill drowners while harvesting the buckthorn.

Revisit bandit camps, sometimes those spots get reused. Stop by the 6 places of power. You might find a water hag or 2 in the swamp in the nw.

As a long rang plan, you should not "free" abandoned sites from monsters/bandits until after you go to Kaer Mohren (prior to patch 1.07 they yielded the same xp to a Geralt at level 1 as at level 35). The same is true about xp from monster dens.