HH's first four levels, are, in all honesty, not that difficult. If you have maxed stats, they should be ezpz, and even if you don't, they're really not much of a challenge. However, maxed stats will help you collect enough eggs in the first four levels, and I'll get to why that's important in a second. I would also HIGHLY RECOMMEND that you max out your jumping capabilities. Again, we'll get to that later. Having 500 spare DNA will allow you to gain superstrength if you press shift. This will make level 5 ridiculously easy. However, it is far from necessary, and if you don't want to do all that grinding, then there are viable ways of completing HH without it. I did it without the use of the 500 DNA cheese, but it took me a bit.

During the first four levels, your focus should be on collecting enough eggs. By the time you get to level 5, you should have at least 150 eggs, which translates to 3 timeshifts. Trust me, you'll need them.

Each level has a gimmick, something that sets it apart from normal levels. The first level, for example, has the pteros carrying pumpkins. These behave as either rocks or eggs, depending on if they are large or small, respectively. Try to collect as many small pumpkins as you can, as these count towards your egg totals and timeshifts. This is a plentiful source of 'eggs', take advantage of it while you can.
Level 2 allows you to fly. Be warned, however, that flying is often slower than running. Only use it if there are large obstacles in the way. Use your flying abilities to get eggs from trees.
Level 3 has a lot of bones, and all the animals are ghosts. Avoid the dark triceratopses, as they are solid obstacles. Everything else you can safely ignore. Pteros still drop eggs; try to get them, as they count as 10 normal eggs in your score.
Level 4 is basically Rampage but with more blood; you have super strength, and can knock aside any animal you come across. Not much to say about this one, except that you should have 3 timeshifts by the time you finish it.
Occasionally you will come across an obstacle that looks like this:
Fall into the gap between the dinosaur's head and the ground, and take the tunnel below out. There are a solid 10 eggs there.

Here it is. The worst that DR has to offer. So hard that it is commonly called 'Doomfingers', after what it does to your hands. Even with maxed stats and three timeshifts I found this a challenge, so be prepared. However, if you know exactly what you're up against, the level will be considerably easier.
This level's gimmick is that you are right next to the wall of doom, and you cannot touch any dinosaur (on this level it will be exclusively stegos.) On Insane difficulty, one touch and the wall overtakes you. Sounds scary, right? It's a lot better if you realize that the wall of doom is just for show. You can stand completely still next to it and it will not harm you. On this level, the only thing that can kill you are the stegos. It took me a long time before I realized this. Don't be like me.
(note: not an actual screenshot. You expect me to take a screenshot on Doombringers?)

The secret to beating doomfingers is DON'T RUSH THROUGH IT. You have all the time in the world, and despite the wall, you are in no danger unless a stego is near. If you see a stego, STOP. Take your time. Find a good angle to jump off of. Make sure that you will not come near the thing. The darkness in the level makes it kind of hard to see, so keep a look out. Remember when I recommended max jumping stats for this level? Use it.
Despite this knoweldge, it is still very easy to make a mistake. This is where the timeshifts come in handy. I sure hope you didn't waste any on the first four levels.
If you are the grindy type that has 500 DNA lying around, then now is the time to use it. The superstrength will activate for the whole level, killing any stego in your path and negating their lethality. This makes you invincible, as the only source of death in this level is taken away. However, this is massive cheesing, and I don't recommend it because a) it takes all the fun out of the thing and b) the amount of grinding you need to do to get 500 DNA is insane. Don't ruin DR for yourself.

If you are really having trouble, try the medium or hard difficulties for practice, or just do other levels for a while in an effort to get better stats / 500 DNA.
/flex
After a few (or a lot of) tries, you should be able to beat it. Congratulations! I hope you found my guide useful. Let me know if there are any errors.