I was looking at some achievement items in TF2, and I found that for a hat, you have to 'level up' your character. What does that mean?
I think you may have meant "Achievement Milestones".
Team Fortress 2 does not have character levels. You could either be confusing between a Steam Profile Level, Strange Item Levels or Achievement Milestones.
Achievement milestones are achievements that you get when you have completed a certain number of achievements in a achievement set (series of achievements for ie. a certain class or event).
As you complete an achievement milestone for a class, you are granted an achievement item at each milestone, or as a reward for completing certain achievements (list below, see wiki for more info)
As for hats:
There are several hats you can earn through achievements:
- Ghostly Gibus - Earn the Ghastly Gibus Grab achievement.
- Mildly Disturbing Halloween Mask - Earn the Candy Coroner achievement.
- Horseless Headless Horsemann's Head - Earn the Sleepy Holl0WND achievement.
- Frontline Field Recorder - Earn the Local Cinema Star achievement.
- MONOCULUS! - Earn the Optical Defusion achievement.
- Full Head of Steam - Complete 7 achievements in the Foundry Pack. (To trigger the Foundry Milestone achievement)
- Gentle Munitionne of Leisue - Complete 7 achievements in the Doomsday pack. (To trigger the Doomsday Milestone achievement)
- Skull Island Topper - Earn the A Lovely Vacation Spot achievement.
Steam Profile Level
Not related to Team Fortress 2 in any way
A steam level is your Steam profile level, which can be increased by:
- Buying more games
- Crafting Badges
- Participating in events
These things you can level up based on the number of kills or times used successfully.
You can level up items with a strange quality (orange name) by killing/using successfully (ie. With Mad Milk, it's the # of enemies soaked using that item). As you reach milestones, its prefix will change from Strange to others, depending on the rank number (and its threshold).
See https://wiki.teamfortress.com/wiki/Strange#Ranks for more information.
However, the leveling in question has to be done in the game Super Monday Night Combat, not Team Fortress 2.
Specifically, Flamingo Kid requires you to reach Level 5 in SMNC, while Triclops requires you to reach level 20 in SMNC.
Incidentally, the level is account-wide in SMNC and can be gotten with any combination of characters. You're awarded experience after every match, although winning a match awards you more XP than losing a match.