Setup:
Sell 2 weapon slots to make this simpler, 4 tomes is fine but primarily just want thorns and some form of hp/hp regen like shield, health, or health regen tome. Disable all tomes you can other than thorns (can also bring armor or xp tome, but this adds more tomes to the pool).
Best way in my opinion is to pick Athena and make sure to never grab weapons or upgrade aegis, at least not its projectile count or attack speed anyway, as they will just kill enemies faster than you can run yourself into them.
Desert tier 1, no challenges. Do not pick up boss curses or difficulty shrines, these will make it significantly harder to get thorns kills off.
In Game:
Simply collect charge shrines, jars, and kill enemies to get xp and upgrades and target movement speed, thorns, and hp upgrades. You do not want any projectile count or attack speed upgrades, as this will activate aegis more and make it harder to get thorns kills.
At 9 and 8 minute marks, a new enemy will start spawning and be added to the spawn pool for the rest of the run, personally, I recommend that you reset if you do not get cactus by your 8 minute spawn mark, as you wont get another new enemy until 5 minutes mark and waiting till then doesn't guarantee you'll even get it then. Most your thorns kills will come prior to the 4 minute mark, after this enemies are varied greatly and spawn a lot, so it can be hard to get thorns off on cacti. Aegis scales with thorns so killing the 7 minute boss should not be hard as long as you did not grab boss curses or difficulty.
Chests are entirely optional for this run in my opinion, i usually only end up getting 3-4 items before i die anyhow, its more about getting a few thorns kills per run, if you do it right, I averaged 20-30 thorns kills per run and managed to complete this in only 10-15 runs (lots of resets from not getting cactus spawns)